Advanced Materials and Technologies for Micro Nano-Devices, Sensors and Actuators (NATO Science for Peace and Security Series B: Physics and Biophysics)

Advanced Materials and Technologies for Micro/Nano-Devices, Sensors and Actuators

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Advanced Materials and Technologies for Micro/NanoDevices, Sensors and Actuators edited by

Evgeni Gusev Qualcomm MEMS Technologies San Jose, California, U.S.A.

Eric Garfunkel

Inst. Advanced Materials, Devices & Nanotechnology Rutgers University Piscataway, New Jersey, U.S.A. and

Arthur Dideikin Ioffe Physical-Technical Institute St. Petersburg, Russia

Published in cooperation with NATO Public Diplomacy Division

Proceedings of the NATO Advanced Research Workshop on Advanced Materials and Technologies for Micro/Nano-Devices, Sensors and Actuators St. Petersburg, Russia 29 June – 2 July 2009 Library of Congress Control Number: 2010921298

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TABLE OF CONTENTS Preface

ix

MEMS/NEMS TECHNOLOGIES AND APPLICATIONS History of Early Research on MEMS in Russia (U.S.S.R.) V. Vaganov

3

Challenges of Complete CMOS/MEMS Systems Integration V. Vaganov

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MEMS for Practical Applications M. Esashi

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Nanochip: A MEMS-Based Ultra-High Data Density Memory Device N. Belov, D. Adams, P. Ascanio, T.-K. Chou, J. Heck, B. Kim, G. Knight, Q. Ma, J.-S. Park, V. Rao, R. Stark, and G. Tchelepi

41

Low Cost Silicon Coriolis’ Gyroscope Paves the way to Consumer IMU B. Vigna, F. Pasolini, R. De Nuccio, M. Capovilla, L. Prandi, and F. Biganzoli

67

Microwave and Millimetre Wave Devices Based on Micromachining of III–V Semiconductors A. Müller, D. Neculoiu, G. Konstantinidis, and T. Vähä-Heikilä Monocrystalline-Silicon Microwave MEMS Devices J. Oberhammer, M. Sterner, and N. Somjit Three-Dimensional Photonic Crystals Based on Opal-Semiconductor and Opal-Metal Nanocomposites V.G. Golubev

75 89

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MEMS DEVICE AND RELIABILITY PHYSICS Pull-in Dynamics of Electrostatically Actuated Bistable Micro Beams S. Krylov and N. Dick Path Following and Numerical Continuation Methods for Non-Linear MEMS and NEMS P.G. Steeneken and J. Stulemeijer

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The Impact of Dielectric Material and Temperature on Dielectric Charging in RF MEMS Capacitive Switches G. Papaioannou

141

ADVANCED PROCESSES AND MATERIALS Development of DRIE for the Next Generation of MEMS Devices H. Ashraf, J. Hopkins, and L.M. Lea

157

Low-Temperature Processes for MEMS Device Fabrication J. Kiihamäki, H. Kattelus, M. Blomberg, R. Puurunen, M. Laamanen, P. Pekko, J. Saarilahti, H. Ritala, and A. Rissanen

167

High-Temperature Stable Au–Sn and Cu–Sn Interconnects for 3D Stacked Applications N. Hoivik, H. Liu, K. Wang, G. Salomonsen, and K. Aasmundtveit 3D Integration of MEMS and IC: Design, Technology and Simulations M.M.V. Taklo, K. Schjølberg-Henriksen, N. Lietaer, J. Prainsack, A. Elfving, J. Weber, M. Klein, P. Schneider, and S. Reitz Low-Frequency Electronic Noise in the Back-Gated and Top-Gated Graphene Devices G. Liu, Q. Shao, A.A. Balandin, W. Stillman, M. Shur, and S. Rumyantsev Modeling of Dry Etching in Production of MEMS A. Rusakov, P. Bystrov, A. Knizhnik, and B. Potapkin XRD and Raman Study of Low Temperature AlGaAs/GaAs(100) Heterostructures P. Seredin, A. Glotov, E. Domashevskaya, I. Arsentyev, D. Vinokurov, A. Stankevich, and I. Tarasov Internal Stresses in Martensite Formation in Copper Based Shape Memory Alloys O. Adiguzel

179 191

205 215

225

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SENSORS Smart Sensors: Advantages and Pitfalls P.J. French

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Vertically Integrated MEMS SOI Composite Porous Silicon-Crystalline Silicon Cantilever-Array Sensors: Concept for Continuous Sensing of Explosives and Warfare Agents S. Stolyarova, A. Shemesh, O. Aharon, O. Cohen, L. Gal, Y. Eichen, and Y. Nemirovsky

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Integration of Diverse Biological Materials in Micro/Nano Devices R. Ghodssi, P. Dykstra, M. Meyer, S. Koev, K. Gerasopoulos, X. Luo, G. Rubloff, W. Bentley, G. Payne, and J. Culver

275

Force Sensing Optimization and Applications J.C. Doll, S.- J. Park, A.J. Rastegar, N. Harjee, J.R. Mallon Jr., G.C. Hill, A.A. Barlian, and B.L. Pruitt

287

Using Parametric Resonance to Improve Micro Gyrsocope Robustness L. Oropeza-Ramos, C.B. Burgner, and K.L. Turner

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Subject Index

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Author Index

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PREFACE A NATO Advanced Research Workshop (ARW) entitled “Advanced Materials and Technologies for Micro/Nano Devices, Sensors and Actuators” was held in St. Petersburg, Russia, from June 29 to July 2, 2009. The main goal of the Workshop was to examine (at a fundamental level) the very complex scientific issues that pertain to the use of micro- and nano-electromechanical systems (MEMS and NEMS), devices and technologies in next generation commercial and defenserelated applications. Micro- and nano-electromechanical systems represent rather broad and diverse technological areas, such as optical systems (micromirrors, waveguides, optical sensors, integrated subsystems), life sciences and lab equipment (micropumps, membranes, lab-on-chip, membranes, microfluidics), sensors (bio-sensors, chemical sensors, gas-phase sensors, sensors integrated with electronics) and RF applications for signal transmission (variable capacitors, tunable filters and antennas, switches, resonators). From a scientific viewpoint, this is a very multi-disciplinary field, including micro- and nano-mechanics (such as stresses in structural materials), electronic effects (e.g. charge transfer), general electrostatics, materials science, surface chemistry, interface science, (nano)tribology, and optics. It is obvious that in order to overcome the problems surrounding next-generation MEMS/NEMS devices and applications it is necessary to tackle them from different angles: theoreticians need to speak with mechanical engineers, and device engineers and modelers to listen to surface physicists. It was therefore one of the main objectives of the workshop to bring together a multidisciplinary team of distinguished researchers. To progress towards overcoming many of these fundamental obstacles, we formulated a workshop, the main goal of which was to develop a better fundamental understanding of the science and technology behind MEMS/NEMS. During the four-day ARW, NATO Country and Partner Country leading researchers met, tutored each other about both their recent results and thinking, and discussed where research and development should be directed. Many of the speakers were from Europe and the U.S. Several key speakers came from NATO Partner Countries including researchers from leading centers in the former USSR (Moscow and St. Petersburg), and Ukraine. The list of researchers represented a diverse international group of recognized scientists and engineers who brought a broad array of backgrounds and strengths into the workshop. The group came from academic, industrial and governmental labs, and had both experimental and theoretical researchers with backgrounds in basic and applied areas of physics, chemistry, mechanical and electrical engineering, surface and materials science. The meeting was organized thematically. Following introductory presentations, the first day concentrated on MEMS/NEMS technologies and market trends, as well as device physics aspects. This day was concluded by a poster session in the evening, giving special priority to younger researchers to present and discuss their work. The second day was dedicated to applications, with leading experts in the

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field discussing progress and sharing their vision for future research. This was followed by a discussion of the important area of sensors for chemical and biological agents. On the last day, we continued with modeling discussions and the role of surfaces, as well as device applications. In the afternoon, a review of NEMS and nanotechnologies was held. The enjoyment of the week came not only from the quality presentations and stimulating discussions, but also from the beauty of St. Petersburg amplified by gorgeous summer weather. The foreigners among us were not only delighted in the “physical” beauty of the city (architecture, Neva-river, canals, palaces, parks, etc.) but enjoyed rich cultural experiences and the hospitality of the local people. The editors would like to thank the members of the International Advisory Committee, Prof. Reza Ghodssi, Dr. Fred Roozeboom, Dr. Vladimir Vaganov and Prof. Alexander Vul’, for help in selecting participants from different countries and for their valuable comments on the scientific program. We would also like to thank all invited speakers and contributors to this book for their support and encouragement during the early planning stages of the Workshop and cooperation in meeting publication deadline. The success of the meeting would not have been possible without the excellent planning and operation of the local team in St. Petersburg led by Dr. Sergey Kidalov and Mrs. Irina Vorobieva. It was a real pleasure to collaborate with this professional team again, after two previous successful NATO ARWs on “Fundamental Aspects of Ultrathin Dielectrics on Sibased Devices: Towards an Atomic-scale Understanding” in 1997 and “Defects in Advanced High-k Dielectric Nano-electronic Semiconductor Devices” in 2005. We are very grateful to Dr. Vadim Siklitsky for developing and maintaining the website (http://www.ioffe.ru/natoarw/2009/) and also for his help during the Workshop. We are thankful to all participants for their excellent presentations, active participation (including peer-review of papers presented in this book) and fruitful discussions at the Workshop. Finally and most importantly, we would like to acknowledge the hard editorial work of Ms. Michele Gardner who helped us to put together the presented papers into this book. The Workshop would not have been possible without financial support from the NATO Public Diplomacy Division. We also greatly appreciate financial contributions from co-sponsors, the Russian Foundation for Basic Research, NT-MDT, and Qualcomm.

August 2009 San Jose, California Piscataway, New Jersey St.Petersburg, Russia

Evgeni Gusev Eric Garfunkel Arthur Dideikin

MEMS/NEMS TECHNOLOGIES AND APPLICATIONS

HISTORY OF EARLY RESEARCH ON MEMS IN RUSSIA (U.S.S.R.) VLADIMIR VAGANOV Siantis Inc, Los Gatos, California 95032, USA, E-mail: [email protected]

Abstract An overview of early MEMS research and developments made in Russia (U.S.S.R.) from 1971 to 1985, which are not widely published and described in the western technical literature, is presented in this paper. Moscow Physics Engineering Institute was the first Russian organization, where MEMS research was initiated. The number of world pioneering developments was made there. Many other institutions in the former Soviet Union participated in early MEMS works. Among them were “Giredmet”, “NiiTeplopribor”, “Electronpribor”, “Nii Physical Measurements”, Bauman Technical University, Novisibirsk University, MIET, Kaunas Polytechnical Institute, Lvov Polytechnical Institute, Leningrad State University and other organizations.

Keywords: Microsensor, pressure sensor, accelerometer, piezoresistor, piezo-transistor, micro-structure, sensitive integrated circuits.

1.

Introduction

The most comprehensive overview of early MEMS history was made by Professor Simon Middelhoek from Delft University in Netherlands [1]. According to him the US academic silicon sensor research was started at Stanford University in 1965. The field of micro-sensors and then MEMS certainly is associated with the term micromachine, which was coined by Professor James Angell from Stanford University in a paper presented at an international conference in 1978 [2]. Thus, Stanford University can be considered as cradle of MEMS. I was fortunate to have the opportunity to visit Stanford in 1969, as a postdoctoral scholar, and sharing the office with Ken Wise who was the first in the world to apply micromachining for making silicon microelectrodes, and who is well known now as one of the leaders in the MEMS area [3, 4]. I was inspired by Jim and Ken and after my returning back to Russia a similar research program at Moscow Physics Engineering Institute (MPhEI) was started. This technical university was a perfect place to start

E. Gusev et al. (eds.), Advanced Materials and Technologies for Micro/Nano-Devices, Sensors and Actuators, DOI 10.1007/978-90-481-3807-4_1, © Springer Science + Business Media B.V. 2010

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because it had the first integrated circuits fabrication facility among Russian universities. This provided an introduction to the new field of micromechanics to Russia. Extensive preceding research on semiconductors in the U.S.S.R. created a solid foundation for MEMS research in Russia.

2. Mechanical sensors As always, at the early stage in any field a lack of either required materials, or chemicals, or equipment often motivates researchers to be more innovative and inventive. At the beginning we didn’t have (100) silicon wafers. That is why researchers at MPhEI started with (111) the available 1″ wafers and developed a piezoresistive pressure sensor based on electro-chemical micromachining (Figure 1a) [5]. From the beginning it was clear that future lie in the complete monolithic integration of sensors and electronics. In 1972 we published a paper describing pressure sensor integrated on one die with IC amplifier (Figure 1b), to our knowledge, the first of its kind in the world [6]. Later sensors integrated with electronics were named “smart sensors”.

(a)

(b)

Figure 1. (a) Piezoresistive pressure sensor based on (111) silicon wafers and electro-chemical micromachining (1972); (b) piezoresistive pressure sensor monolithically integrated with differential amplifier (1972).

By 1972, with access to (100) silicon wafers and starting research in anisotropic etching of silicon, we fabricated piezoresistive pressure sensor with the peripheral location of longitudinal and transverse piezoresistors along the sides of a square diaphragm (Figure 2a) [7]. Next the piezoresistive pressure sensor with peripheral location of four complete bridges in the center of four sides of a square diaphragm was also fabricated (Figure 2b) [8].

HISTORY OF EARLY RESEARCH ON MEMS

(a)

5

(b)

Figure 2. (a) Piezoresistive pressure sensor on (100) Si, square diaphragm and peripheral piezoresistors (1972); (b) pressure sensor with four Wheatstone piezoresistive bridges (1974).

Access to hydrazine hydrate in addition to KOH allowed researchers to make a two-side anisotropic etching and make a first prototype of piezoresistive accelerometer from a pressure sensor by etching a slot along three sides of the diaphragm from the front side of the wafer in 1974 (Figure 3a) [9]. As one can see, this accelerometer was made from the pressure sensor developed earlier and shown in the Figure 2b. The slot along the three sides of the diaphragm from the front side of the die was etched and thus a cantilever beam made from the diaphragm with the complete bridge circuit in the area of clamping the cantilever was fabricated. Visiting Stanford again in 1975 I spent some time with Jim Angell’s group sharing our experience in MEMS research and in accelerometers in particular [10]. I made the first MEMS accelerometer dedicated design and fabricated this accelerometer as shown in Figure 3b. The first publication of this device was made in Russia in 1978 [11]. Later, a similar accelerometer was made at Stanford and publication of its microstructure in “Scientific American” in 1983 is well known [12]. It is interesting to notice that sensitivity of these first accelerometers was high enough that during experiments with it was noticed that it was picking up a sound due to its small thickness and large area. It certainly was acting as a microphone although frequency bandwidth was limited to several kilohertz. Among other interesting early developments was a microstructure of an accelerometer with four symmetrical beams and an asymmetric proof mass published in 1983, as shown in Figure 3c [13]. Similar microstructures were incorporated in 3-axis piezoresistive accelerometers, which are still in use [14–16]. That time market was not ready yet for even one-axis accelerometers not mentioning threeaxis devices. As known, the real market demand for MEMS accelerometers was for air bag automotive applications at the beginning of 90th and the first air bag accelerometers were piezoresistive, though later they were pushed out by capacitive devices.

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(a)

(b)

(c)

Figure 3. (a) First accelerometer prototype made from pressure sensor in 1974; (b) first piezoresistive accelerometer with cantilever beam and full bridge in the beam clamping area (1975); (c) microstructure of accelerometer used later for multi-axis measurements (1983).

From the beginning our efforts were focused not only on piezoresistors but also on piezo-transistors and other silicon devices, which principle of operation is based on mobility of charge carriers. In 1975 we designed and fabricated pressure sensors based on bipolar and MOS transistors shown in Figure 4 [17–19]. Bipolar transistors were located in different areas of the silicon diaphragm and were planar n-p-n and lateral p-n-p type. Each transistor had separate connections to different contact pads, which provided an opportunity to investigate the piezosensitive property of all transistors independently. MOS transistors were p-channel transistors with different locations and orientation of the channels.

(a)

(b)

(c)

Figure 4. (a) Pressure sensor die with bipolar n-p-n and p-n-p piezo-transistors as sensitive components; (b) pressure sensor die with p-channel MOS piezo-transistors; (c) first piezo-sensitive circuit combining piezo-transistors and pizoresistors (1975).

HISTORY OF EARLY RESEARCH ON MEMS

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There were several reasons why our attention was attracted to piezo-transistors. The size of a transistor is much smaller than the size of a resistor with the potential to dramatically scale overall sensor size down. The transistor is a three port-pole component compared to a resistor, which is a two port-pole component. Therefore, in contrast with resistors, which can be combined in a Wheatstone bridge circuit with only four sensitive components, transistors can be combined in a circuit with unlimited number of sensitive components and thus increase sensitivity of a sensor. Finally, a sensitive transistor can also be used for an amplification of a transduced signal. In 1973 the Russian patent was filed and issued in 1975 for the first piezo-sensitive integrated circuit shown in Figure 4c [20]. Other researchers in Russia, from Novosibirsk University in particular, also were investigating the properties of sensors based on MOS piezotransistors reporting about sensor, which had a bridge circuit combined from longitudinally and transverse positioned transistors relative to applied mechanical load [21].

3. Sensors for biomedical applications In early years in different countries many MEMS projects were related to biomedical applications due to a very small size of the sensors. In 1973 the first lateral catheter pressure sensor was introduced [22]. The pressure sensitive diaphragm didn’t have a face-end location, as it was previously made, but it was parallel to the axis of the catheter (Figure 5a). The sensor die had two silicon micro-profiled parts: first one having a square diaphragm with piezoresistor bridge electrically connected to contact pads and a cap bonded to the first part.

Figure 5. (a) Catheter pressure sensor die with lateral position of the diaphragm relative to longitudinal catheter axis and with silicon cap providing channel for external pressure through the catheter (1973); (b) multi-beam sensor for cochlear prosthesis (1976).

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Based on the observation that beam-type sensors exhibit property of a microphone another bio-medical project was started and a die with multiple beams having different geometry was developed in 1976. It provided different mechanical resonant frequency of the beams and reacted differently on a sound of different frequency (Figure 5b) [23]. The goal was to create a prototype of cochlear prosthesis. It was an ambitious goal, which didn’t find a financial support and the project was abandoned. Biomedical applications of MEMS sensors enabled early recognition of the importance of micro-packaging at the wafer level. The development of submillimeter catheter pressure sensors for neuro-surgical applications, shown in Figure 6, is a good example [24]. The die was only 700 µm wide and had a rectangular diaphragm 300 µm wide, 800 µm long and 7 µm thick. It also had two longitudinal bosses and all four piezoresistors were transverse: two resistors were located on two peripheral thin parts of the diaphragm and two resistors on central thin part of the diaphragm, as shown in Figure 6a. The silicon cap beside the cavity on the top of the diaphragm had a micro-socket for connecting and soldering micro-wires to contact pads on the sensor die. After bonding the wafers, they were diced into separate dice ready for assembling with the micro-wires. The ends of long wires were inserted into a micro-socket, the solder or conductive epoxy was loaded through the loading windows and then all wires were soldered simultaneously. Sensor die chips from both sides and a cap chip are shown in Figure 6b. The sensor die was assembled in an external stainless steel package – the tip of the catheter was only 1 mm in diameter and it was used in a number of medical experiments including intra-brain pressure measurements in brain tumor patients.

(a)

(b)

Figure 6. (a) Catheter pressure sensor die for biomedical applications had micro-packaging at the wafer level including micro-socket for connection to the long wires; (b) view of chips of a sensor die from both sides and a cap with micro-socket (1978).

Many other interesting projects related to biomedical applications of microsensors were conducted that time. One was dedicated to the development of artifi-

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cial heart [25]. Figure 7a illustrates an early prototype of artificial heart with radioisotope power supply. The control system of the heart used several pressure sensors of different ranges and package configurations. Extra-vessel blood pressure sensor, shown in Figure 7b, was developed for prolonged chronic testing of the blood pressure in arteries and veins. The sensor was applied to the external wall of the blood vessel and easily fixed around the vessel [26]. Extra-cellular microelectrodes similar to those, what Ken Wise made at Stanford, were developed and fabricated for neuro-physiological research (Figure 7c) [27].

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(b)

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Figure 7. (a) Prototype of artificial heart with radioisotope power supply and control system comprising multiple pressure sensors (1979); (b) extra-vessel blood pressure sensor (1983); (c) extra-cellular micro-electrodes (1975).

Researchers from Kaunas Polytechnical Institute also developed silicon microsensors for blood pressure measurements [28]. Another interesting development of miniature pressure sensors for biomedical applications was made in Zelenograd. This sensor was made on the silicon-on-sapphire (SOS) structures [29]. The unique process technology of local micromachining of sapphire wafers was developed, which allowed using this technology not only for biomedical sensors but also for industrial applications. Good chemical resistance of sapphire diaphragm provided high reliability of these sensors. “NIKIMP” also was developing medical sensors based on monocrystalline silicon piezoresistive strucrures in the form of a micro-frame made from silicon and mounted on pressure diaphragm [30].

4.

R&D of micro-sensors theory and micromachining processes

Much of the early work between 1972 and 1985 was focused on development of theory, design foundations and processes for mechanical sensors. In particular, the research on anisotropy of piezoresistive coefficients in silicon wafers of different

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orientations was published in 1978 [31]. Within several years extensive analysis was conducted on the sensitivity of piezoresistors p and n type with different angular orientation and position on the springy elements of different shape and crystallographic orientation was conducted. Square, circular, rectangular, octagonal, cylindrical, flat and profiled in thickness springy element were analyzed. As a result, the design concepts and design rules for different electro-mechanical microsensors were developed [32–34]. There were many industrial and academic research institutes, which traditionally developed conventional transducers based on strain gages including semiconductor strain gages. Having large experience in this area it was relatively easy for them to make a gradual transition into a micro-sensor area at least at the theoretical and metrological level. Among those organizations were “Nii Machinovedenia” of Academy of Sciences of the USSR, “Giredmet”, “Nii Teplopribor”, “NIKIMP” and others. Among educational institutions the pioneering research in micro-sensors was conducted in Technical University named after Bauman, Novosibirsk University, Moscow Institute of Electronic Technology (MIET), Leningrad University, Leningrad Polytechnical Institute, Kaunas Polytechnical Institute and many others. All those organizations significantly contributed to the development of theory, fabrication technology, packaging and testing of different microsensors. Early understanding of the importance of all aspects of micro-sensors: microstructure and sensitive components; IC circuitry for signal conditioning and processing; micro-packaging; testing; their interdependence through the desired parameters and characteristics of resulting micro-device lead us to developing so-called “system approach to MEMS design and commercialization”, which later helped in real life cases of commercialization and which was described in several later publications [35, 36]. Among early micromachining technologies anisotropic etching of silicon certainly attracted a lot of attention. At MPhEI extensive research on anisotropic etching of silicon including a very detailed study of multidimensional space of anisotropy of etching rate vs type of etchant, concentration of etching components, and the temperature of the process was done during this period [37, 38]. Figure 8 illustrates some of the indicatrixi obtained during this research. This effort resulted in development of a model of anisotropic etching of silicon based on a phenomenological approach and a model for computer simulation of the process of local anisotropic etching through a mask of arbitrary shape on the wafers of different crystallographic orientation [39, 40]. One of the particular results of this research was development and patenting of the set of geometrical shapes of right corner compensation masks needed for anisotropic etching of convex-shaped microstructures on (100) silicon wafers [41–43].

HISTORY OF EARLY RESEARCH ON MEMS

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(b)

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Figure 8. Indicatrix of anisotropic etching of silicon in water solution of KOH 20% at 50°C (a); KOH 30% at 50°C (b); and in hydrazine hydrate at 50°C (c) (1975).

At Moscow Institute of Electronic Technology (MIET) the researchers attacked anisotropic micromachining of silicon not only in alkaline solutions but also in acid solutions. In a presence of ultrasound, which reduced the diffusive limitation of chemical reaction, the reaction became anisotropic in the nitric and hydrofluoric acid solutions known as isotropic and polishing [44]. As the major research and development activity in MEMS area was happening within an educational institution, it was natural to implement the results of this research into the educational process. In 1976 the first course of lectures on MicroSensors was delivered to graduate students at MPhEI. In 1980 and 1981 two text books for students were published at MPhEI on “Microelectronic transducers” and “IC transducers” respectively (Figure 9a, b) [45, 46]. In 1983 the first monograph on IC piezoresistive sensors was published by Russian technical publishing house “Energoatomizdat” (Figure 9c) [47]. This book was one of the first books in the area of microsensors. Unfortunately it was published only in Russian and naturally didn’t have world wide circulation. In Russia however this book is still in the list of recommended literature for graduate students in MEMS area at the universities.

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Figure 9. (a) Text book “Microelectronic transducers” (1980); (b) text book “IC transducers” (1981); (c) monograph “IC Piezoresistive sensors” (1983).

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Other developments and industrially manufactured sensors

Many organizations were involved in research and development of other than piezoresistive mechanical sensors. Institute of Solid State Physics and Semiconductors of Belorussian Academy of Sciences developed magneto-sensitive Hall sensors on InSb and GaAs shown in Figure 10a [48]. Another magnetic sensor with digital output based on silicon developed by a group of Moscow researchers is shown in Figure 10b [49]. Figure 10c illustrates silicon capacitive pressure transducer developed in Leningrad State Technical University [50].

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Figure 10. (a) Hall sensor on InSb; (b) integrated magnetic field sensor with frequency output; (c) silicon capacitive pressure transducer.

There were several organizations, which not only conducted research and development of micro-sensors but also commercialized their developments in volume production. “Nii Teplopribor” developed series of silicon-on-saphire (SOS) pressure sensors “Crystal” in 1973 in cooperation with Zelenograd’s semiconductor company and started their production manufacturing in 1974 [51]. Transducers “Sapphire” and “Sapphire 22” included gage, absolute and differential pressure, consumption of liquids and gases, and liquids level [52]. Transducers were developed for applications in harsh environment and provided accuracy 0.1–0.25% in the temperature range –50 ° C to 120°C. “Nii Physical Measurements” in Penza with participation of MPhEI developed 11 types of pressure transducers for aero-dynamic applications. High quality of these devices allowed them to be used in Russian Shuttle Buran. Sensor dice for these sensors, which were manufactured serially, are shown in Figure 11a. Another Russian company “Electronpribor” in St. Petersburg developed together with MPhEI low cost pressure sensors for automotive applications and started its manufacturing in 1989. These sensors shown in Figure 11b had a low cost plastic package and thin-film trimming resistors on a ceramic substrate for individual calibration of sensor’s offset and sensitivity. Sensor chips were anodically bonded with a glass substrate before packaging.

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Figure 11. (a) Serial pressure sensors for aero-dynamic applications (1983); (b) pressure sensor for high volume automotive applications (1989).

6.

Conclusion

In 1991 the Editor-in-Chief of “Sensors and Actuators”, Prof. Simon Middelhoek, initiated a publication of a special issue devoted to current research on physical sensors in the U.S.S.R. [53]. I had an honor to be invited as a guest editor of this issue, which covered the geography: Moscow, Leningrad, Odessa, Uljanovsk and Yoshkar-Ola. This issue also presented the spectrum of sensors developed in Russian universities and in industry: mechanical sensors on silicon and silicon-onsapphire, phototransistor arrays, liquid crystal sensors, magnetic field sensors, hydrogen detectors, pH-ISFET, SAW sensors and SOI high-temperature sensors. Although that issue made the first presentation of Russian MEMS activity to the western world it didn’t present the whole picture of Russian R&D in MEMS area of that time and didn’t describe the preceding research. This paper hopefully fills in some of the gaps of that presentation. It also should be understood that reconstruction of the events, materials and publications of almost 40 years old is always a challenging task and the author is relying on the leniency of a reader in possible inaccuracy of presented materials. Author also would be grateful for any comments, corrections and response. Today’s broad resources of international communication including Internet hopefully will facilitate the process of exchanging knowledge in the Micro and Nano technologies more effectively and facilitate initiation of new scientific and commercial contacts between the Western, Eastern and Russian professionals in these areas.

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References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.

Simon Middelhoek, Celebration of the tenth transducers conference, Sensors and Actuators, 82 (2000) 2– 23 Stanford News Service, News Release February 28, 2006 Kensall D. Wise, James B. Angell, Arnold Starr, An Integrated-Circuit Approach to Extracellular Microelectrodes, Biomed. Engineering, IEEE Trans. on. 08/1970; BME-17(3) Dr. Kensall D. Wise, William Gould Dow Distinguished University Prof. of Electrical Engineering & Computer Science, www.nae.edu/nae/naepub.nsf/Members USSR Pat. 458720. Diaphragms fabrication technique of miniature planar epitaxial pressure sensors (V.I.Vaganov,K.M.Ponomarev), B.I. 1974 #46 Vaganov V.I., Ponomarev K.M., Silicon strain gage component for IC pressure sensors, Physical Electronics, Kaunas, KPI, 1972, v.1, 125– 130. (in Russian) Vaganov V.I., Polivanov P.P., Ponomarev K.M., IC pressure sensor for biomedical applications, Tenzometriya-72, Digest of All-Union Conf. Methods and Means in Strain Gauge Measuremens, Sverdlovsk, 1972, M., IMASH AN USSR, 1972, (in Russian) Vaganov V.I., Polivanov P.P., Ponomarev K.M., IC pressure sensor for biomedical applications, Izvestia Vuzov, ser. Radioelectronics, v.XVII, 1974, 107– 109 (in Russian) Development and Research of ICs based on new semiconductor devices, Annual Report on Government Project “Mayak”, v 2, State Reg. # 75026315, MPhEI, 1974 (in Russian) V.Vaganov, Suggested Improvements on Accelerometer, Office memorandum to Professor J. Angel and Professor J. Meindl, Stanford University, April 30, 1975 V.I.Vaganov, N.I.Goncharova, IC cantilever beam sensor of mechanical parameters, Electronic Instrumentation Technique, Atomizdat, Moscow, 1978, #1, (in Russian) James B. Angell, Stephen C. Terry, Phillip W. Barth, Silicon Micromechanical Devices, Scientific American, April, 1983, 44– 55 Vaganov V., Micromachining is Trend for Sensors, Components and Systems in Instrumentation, Energoatomizdat, Moscow, 1983, pp. 3– 9. (in Russian) K. Yamada, K. Higuchi, H. Tanigawa, A novel silicon accelerometer with a surrounding mass structure, Sensors and Actuators, A21-A23, 1990 308– 311 US Pat. 5,894300, Silicon bulk micromachined, symmetric, degenerate vibratory gyroscope, accelerometer and sensor and method of using the same, Tony K. Tang et al, 1999 US Pat. 6662659, Acceleration sensor, Masakatsu Saitoh, 2003 Development and Research of ICs based on new semiconductor devices, Annual Report on Government Project “Mayak, v 3, State Reg. # 75026316, MPhEI, 1975. (in Russian) V.I.Vaganov, V.V.Beklemishev, A.V.Sumin, IC pressure sensors on planar piezotransistors, Tenzometriya-76, Digest of All-Union Conf. “ Methods and Means in Strain Gauge Measurements and their Applications” , Kishinev, 1976 (in Russian) V.I.Vaganov, P.P.Polivanov, IC piezotransistor pressure sensor, Electronnaya Technika, 1975. ser. 11, #4, 89-92. (in Russian) USSR Pat. 491059. Microelectronic pressure sensor, (V.I.Vaganov), B.I. #41-1975. E.I. Makarov, et al., IC piezosencitive circuits on MOS transistors, Tenzometriya-76, Digest of All-Union Conf. “ Methods and Means in Strain Gauge Measurements and their Applications” , Kishinev, 1976 (in Russian) Development and research of pressure sensors for intraheart catheterization, Final report, MPhEI, Moscow, 1973. (in Russian) Research and Development of IC sensors for biomedical applications, Annual Report, State Reg. # 77021585, MPhEI, Moscow, 1976. (in Russian) V.I.Vaganov, V.V.Beklemishev, S.G.Geletsyan, N.I.Goncharova, A.B.Noskin, IC pressure sensor with ion implanted piezoresistors, Sensitivity Theory in Electronic and Electrical Systems, digest, All-Union Scien.Conf., M., MIEM, 1978, 27– 28. (in Russian) V.A.Kremnev, V.B.Parshin, A.V.Sumin et al., A transducer choice for an implantable autonomous artificial heart, Modern Problems of Transplantation and Artificial Organs, MZ USSR, 1979, 146– 149. (in Russian)

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26. V.I.Vaganov, V.V.Beklemishev, V.S.Baranov, Implantable contact sensor of arterial blood pressure, Metrology of measurements in medicine, Tallin, 1983, 137. (in Russian) 27. V.I.Vaganov, B.V.Tkachev, IC metallic microelectrodes of comb-like structure, 7-th AllUnion scien.-techn.conf. on microelectronics, digest, Lvov, 1975. (in Russian) 28. I.B.Baltavichus, et al., Sensors for blood pressure measurements, 7-th All-Union scien.techn.conf. on microelectronics, digest, Lvov, 1975. (in Russian) 29. Aleksa A.G., Zimin V.N., et al., Electronnaya Technika Electronic technology, ser. 11, vol. 2, 43– 46, 1976. (in Russian) 30. A.A. Tzivin, U.M. Bazgin, T.A. Motorigina, Biomedical transdusers on monosrystalline structures, 7-th All-Union scien.-techn.conf. on microelectronics, digest, Lvov, 1975 31. V.I.Vaganov, V.M.Khudikina, Anisotropy of piezoresistive coefficients for IC sensors of mechanical parameters, Electronic Measurement Technique M., Atomizdat, 1978 32. N.I.Goncharova, A.B.Noskin, Sensitivity topograms of piezoresistors of IC pressure sensors, Electronic Instrumentation Technique, M., Energoizdat, 1981, #3, 18– 23 33. V.V.Beklemishev, V.I.Vaganov, Non linearity analysis of IC pressure sensor with a square diaphragm,“ Transducers based on microelectronic technology” , Moscow, 1983 34. V.I.Vaganov, N.I.Goncharova, I.I.Sluchak, IC piezoresistive sensor with flexible elements of complex forms, Electronic Measuring Devices and Systems, M., Energoatomizdat, 1984, 105– 108 35. V.I.Vaganov, Basic trends and development problems in sensoelectronics and system approach to sensor and actuator design, Proc.Conf. “ Transducers based on microelectronic technology” , M., MDNTP, 1986, 3– 16. (in Russian) 36. V. Vaganov, A System Approach to Photonic MEMS Commercialization, Fiberoptic product news, Nov, 2002 37. V.I.Vaganov, P.P.Polivanov, Local anisotropic etching of silicon for fabricating IC pressure sensors, Electronnaya Technika, 1975, ser, Complex miniaturization of radioelectronic devices and systems, #4, 93– 98 38. V.I.Vaganov, N.I.Goncharova, T.S.Plokhova, Study of dependance etching rate for anisotropic etching of silicon in KOH water solutions versus etching regime. Electronnaya Technika, 1980, ser, Microelectronics, No2, 29– 36 39. V .I.Vaganov, T.S.Plokhova, Study of shape dynamics for local anisotropic etching of silicon. Electronnaya Technika, 1979, ser. Microelectronics, #5, 55– 62 40. Belov N.S. Silicon micro-mechanical structures, Ph.D. dissert., Moscow, MPhEI, 1989. 41. USSR Pat. 795326. Protective mask, (V.I.Vaganov, T.S.Plohova), 1980 42. USSR Pat. 858491. Protective mask for batch chemical separating of monocrystalline (100) wafers into chips, (V.I.Vaganov, T.S.Plohova), 1980 43. USSR Pat. 1220516. Protective mask, (N.S.Belov, V.I.Vaganov), 1985 44. A.I. Buturlin, T.I. Vishneva, U.D. Chistiakov, Ultrasound activated process of anisot ropic etching of silicon in acid solutions, Digest of projects, Moscow, MIET, 1980 45. V.I.Vaganov, Microelectronic sensors, text book, MPhEI, Moscow, 1980. (in Russian) 46. V.I.Vaganov, IC sensors, text book, MPhEI, Moscow, 1981, 77. (in Russian) 47. V.I.Vaganov, IC piezoresistive sensors, Energoatomizdat, Moscow, 1983. (in Russian) 48. Hall microsensors on InSb and GaAs epilayers, Catalog, Institute of Solid State Physics and Semiconductors, Belorussian Academy of Sciences, 1983 49. S.V. Gumenuk, B.I.Podlepetsky, et al.,Integrated magnetic sensor with frequency output, Sensors and Actuators A, v 28, No3, 1991 50. V.M. Artyomov, E.A. Kudryashov, et al., Silicon capacitive pressure transducer with increased modulation depth, Sensors and Actuators A, v 28, No3, 1991 51. G.G. Iordan, Kenigsberg V.L., et al., Semiconductor piezoresistive transducers, Digest of All-Union Conf. “ Methods and Means in Strain Gauge Measurements and their Applications” , Kishinev, 1976 (in Russian) 52. Kenigsberg V.L., Stuchebnikov V.M., et al., Izmeritelnaja Technika, #10, 1978 53. Sensors and Actuators, A special issue devoted to Current Research on Physical Sensors un the U.S.S.R., Guest Editor: V.I.Vaganov, volume A28 No.3, August 1991

CHALLENGES OF COMPLETE CMOS/MEMS SYSTEMS INTEGRATION

VLADIMIR VAGANOV Siantis Inc, Los Gatos, California 95032, USA, E-mail: [email protected]

Abstract This paper is dedicated to the analysis of the needs and challenges of integration of CMOS and MEMS. It is acknowledged that individual sensors era is ending and the multi-sensor micro-systems era is beginning. On the example of cost requirements for IMU for high volume cell phone application it is demonstrated that achievement of required cost target is possible with monolithic MEMS CMOS integration. Among major challenges of this integration are: need for sensors sensitivity increase, as the way to scale their size down; process integration for different sensors and compatibility of this process with CMOS fabrication technology. General description of Siantis’ technology, which met all major challenges of monolithic integration, is presented then. Finally, economic justification for monolithic integration is considered.

Keywords: CMOS MEMS integration, pressure sensor, accelerometer, piezoresistor, piezo-transistor, micro-structure, multi-sensor micro-systems, inertial measurement unit, sensitive integrated circuits, principle of multi-axis measurements.

1. Need for monolithic integration Even before the term “MEMS” was coined and established, some of the early pioneers in this field envisioned ultimate monolithic integration of MEMS and ICs. Over three decades has passed and this is not yet a main stream technology in MEMS. However, the most significant MEMS products, like print-heads, ADI’s accelerometers, TI’s DLP, are utilizing monolithic integration. Their commercial success is the best evidence of this ultimate technological goal. Nobody is arguing today that integration of MEMS and sensors in particular with CMOS is the next natural step in micro-technology evolution. Many researchers and companies are working in this direction addressing specific devices, applications and markets. Very good example of this effort is an initiative of Ken Wise, who founded Engineering Research Center for Wireless Integrated MicroSystems (WIMS) funded by NSF in 2000. The center combined efforts of E. Gusev et al. (eds.), Advanced Materials and Technologies for Micro/Nano-Devices, Sensors and Actuators, DOI 10.1007/978-90-481-3807-4_2, © Springer Science + Business Media B.V. 2010

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about eight universities in creating microsystems capable of measuring a variety of physical parameters, interpreting the data and communicating over a wireless link [1]. The dramatic difference between what the market was looking for yet several years ago and now is the need for simultaneous measurements of multiple parameters of different physical and/or chemical domains. Several examples of these market needs are shown in Figure 1.

Figure 1. Examples of market need in micro-systems measuring multiple parameters.

It becomes obvious that Individual Sensors Era is ending. Multi-Sensor MicroSystems Era is beginning. Why is it happening now? The market is ready to accept and utilize huge amount of such systems for different high volume applications – market pull. The underlying technologies are developed enough to push the market. These are technologies in all three areas: sensing, computing and communicating. However, for all massive applications the major requirements are: low cost, small size, high reliability. What kind of integration monolithic or hybrid would be better? Older generation of semiconductor industry professionals might remember that at the beginning of IC there were a lot of discussions about “monolithic” vs “hybrid” integration. The real life put everything on its place and brought an understanding that both approaches have the right to live depending mainly on the size of the market and related cost requirements.

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Principally the history is repeating itself on the example of MEMS and CMOS integration. There are the same two basic approaches: hybrid (MCM) and monolithic, although the border between those two is fading with the advance of new technologies and processes. For example, when two silicon wafers, one with CMOS and another with MEMS, are bonded at the wafer level, it is certainly not a traditional hybrid integration but although not yet true monolithic. To add here chip-scale packaging (CSP), wafer-level packaging, through silicon vias (TSV), vertical multi-chip packaging, and we have even fuzzier line between two basic integration approaches. So the correct question should be not “Which MEMS/CMOS integration technology is better?” but rather “When different MEMS/CMOS integration technologies should be used?” By the other words the question should be: “When monolithic integration should be used instead of MCM, assuming that all technological issues of this integration are resolved for a given application?” Let us consider an example of cost requirements for portable devices. How low the cost, how small the size and how high the reliability should be for these multi-sensor micro-systems depends on specific applications. For example, very high volume cell phone market is looking now for not just 3-axis accelerometer, which is already started to be implemented in some high-end phones, but for whole inertial measurement unit (IMU) for many potential applications, as shown in Figure 1. In particular it can be used for navigation assisting GPS between the transmissions and for navigation in the areas shielded from radio signals. Such multi-sensor micro-system should comprise at least three different sensors: 3-axis linear accelerometer, 3-axis angular sensor, 3-axis compass and CMOS processing circuitry. In some other requirements it also might have an altimeter for measuring elevation, for example within a building. Figure 2 illustrates the pie-chart of the six most important cost components including packaging and testing. Sooner or later this technology will penetrate into all cell phones. It was reported that the bill of materials (BOM) for the low-end cell phones is approaching $20. Let us aggressively assume that the cost of new component might be allowed at 10% of BOM, e.g. $2. Let us also assume for the sake of discussion that this total cost of IMU will be equally broken down between six cost components. Then each of the 3-axis linear accelerometer, 3-axis angular sensor, 3-axis compass, CMOS, packaging and testing should cost $0.33. Is it realistic to achieve this low cost for all these separate components? The answer is “definitely not” without integration. Is it realistic to achieve this low cost with hybrid (MCM) integration? I would say: “Doubtfully” because there is no evidence that within the existing trend of scaling down the size and therefore the cost of 3-axis accelerometers and gyro the price $0.33 per chip-packaged 3-axis device could be achieved soon. Is it realistic to achieve this low cost with monolithic integration? The answer is “definitely yes”. More than that, the monolithic integration seems to be the only way to achieve this goal for such high volume application.

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Figure 2. Cost structure of the inertial measurement unit components.

2. Major challenges of monolithic integration What are the major challenges for achieving monolithic integration of MEMS sensors with CMOS? The first and probably the main challenge is how to decrease the size (area) of the sensors shared with CMOS at the surface of the die. There are several obvious reasons for that. Multiple sensors require overall size reduction. Integration with IC and wireless requires smaller sensor size. Lower cost requires smaller size. But smaller sensors size typically infers lower sensor sensitivity. For a given application the required sensitivity is determined and therefore, the size of the sensor for a given technology is also determined. If sensor sensitivity can be increased with a new technology, then the size of the sensor can be decreased while still providing the required sensitivity. The second challenge is different sensors process compatibility, meaning how to develop such fabrication process, which would allow fabrication of different multi-axis sensors at the same time. The third major challenge is the selection of such additional materials and processes required for fabrication of different sensors that are CMOS process compatible, which would manifest MEMS CMOS monolithic integration. Siantis successfully met all three major challenges of CMOS and sensors monolithic integration by: 1. Decreasing sensors size and providing their future scalability by increased sensitivity. 2. Providing unified sensing and processing components platform and novel microstructures. 3. Developing unified fabrication process for different sensors. 4. Using monocrystalline silicon as both a mechanical material for microstructures and a substrate for electronic components and also developing a two-stage process (CMOS first, MEMS second) allowing monolithic integration of CMOS with different sensors.

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Foundation of Siantis’ Technology for Sensitivity and Functionality Increase/ Size and Cost Decrease comprises: 1. Big mechanical input element relative to small sensor size – Novel Microstructures. 2. Multiple sensitive components within multiple suspensions and Simple Microstructure for multi-axis measurements. 3. CMOS transistors as both sensitive and processing components – Unified Component Platform. 4. Collecting more energy induced by measurand – Sensitive Integrated Circuits.

3. Novel microstructures On the example of mechanical sensors, such as accelerometers and gyros, let us look at the important criteria for their mechanical microstructures for the purpose of increasing their sensitivity and scaling size down. Table 1 summarizes these requirements. TABLE 1. Requirements for mechanical sensors microstructure.

Bigger proof mass High sensitivity High resolution Small mechanical noise Better mass reproducibility Stronger suspension Sensor size scaling

Stronger silicon suspension High reliability High shock protection No stiction Wide frequency bandwidth High long-term stability High yield

Simple mechan. structure High reliability Better stability Sensor size scaling

There are many limiting factors for scaling down mechanical sensors. Physical principle, fabrication technology, microstructure and noise are among them. For example, all existing capacitive MEMS sensors have serious challenges in their ability to be significantly scaled down. Any multi-axis sensor cannot be smaller than its several sensitive components. All sensitive components of capacitive sensors are capacitors and they all are located at the surface of the sensor due to “surface micromachining”. These capacitors and the relative change of the capacitance are practically reached the physical limit. Capacitance value could be in the range of several fF and the measured change of capacitance corresponds to a measured charge smaller than the charge of one electron (by statistical measurements) [2]. Small capacitance and its change, on one end, and charge of electron, on the other end, make it very challenging to provide a wide dynamic range of the sensors in concert with scaling them down. If the goal is decreasing of the area occupied by the sensor microstructure at the surface of the die, then the only way to increase the capacitance and its relative change is to increase the thickness of the surface micro-machined layer keeping the length and the width of the fingers in the comb structures and the width of the gaps between the fingers the same. However due to the limits on the aspect ratio during DRIE it is very challenging to achieve this

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goal [3]. Increasing the depth of DRIE etching would also require increasing the gaps between the fingers, which would not result in increasing the capacitance and its relative change, as capacitance would increase proportionally to the depth and inversely proportionally to the gap width. In reality it would result in increasing the area of microstructure at the surface of the silicon die. Therefore, it seams that MEMS surface micro-machined capacitors cannot be significantly scaled down in size, as well as capacitive MEMS sensors. The second serious challenge of scaling capacitive sensors is that it is not easy to make a big proof mass due to the nature of surface micromachining. The device layer is thin and the mass of the device micro-structure is determined by the area occupied by the microstructure at the surface of the die, which one wants to scale down. Of course, some new technological opportunities like SiGe films, which can be deposited at low temperature on the top of already fabricated CMOS circuit and which can be used as a structural material of the capacitive micro-structures, could make for some time less critical the issue of scaling down the size of capacitive sensors, while the other issues including complexity of the structure, small mass and the economy of this integration will still remain [4]. Figure 3 illustrates the relative size and mass of the proof mass of the current capacitive sensors compared to Siantis’ sensors.

Figure 3. Size and proof mass of the current capacitive sensors compared to Siantis’ sensors.

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(a)

(b)

(c) Figure 4. (a) First generation of Siantis 3-axis accelerometer; (b) micro-photograph of the mechanical microstructure elements; (c) second generation of 3-axis accelerometer.

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If capacitive sensor occupies 1 mm2 area and the device layer is 2 μm thick, then the proof mass would be about 1 µg. First generation Siantis’ sensors occupy 0.1 mm2 and the proof mass is 54 µg. The second generation Siantis’ sensors occupy 0.01 mm2 and have the proof mass of 100–400 µg. The result is that Siantis’ sensors are more than 100 times smaller at the surface of the die shared with CMOS and at the same time have proof mass more than 100 times bigger. Figure 4a illustrates the first generation of Siantis 3-axis accelerometer [5]. The microphotographs of the die, mechanical microstructure of the proof mass and one of the beams are shown from the back side in Figure 4b. Figure 4c illustrates the second generation of 3-axis accelerometer, where microstructure of the sensor occupies a small area at the surface of the die shared with CMOS and the big proof mass providing large sensitivity is located within the thickness of the wafer [6].

4. Simple microstructurs for multi-axis measurements General principle, which Siantis uses for multi-axis measurements, is that the large proof mass is formed within thickness of the silicon wafer rather then by depositing structural layers on the surface of the wafer. The proof mass is connected by multiple suspensions to the frame of the die and multiple sensitive elements are incorporated within those suspensions, as schematically shown in Figure 5.

Figure 5. Generalized principle of multi-axis measurements.

The proof mass might move in different directions relative to the frame depending on the vector of the mechanical parameter to be measured. As the mass is not directly connected to the sensitive components, it might have no restrictions on arbitrary motion in any direction. The combination and the value of the output signals from different sensitive components, as a result of mechanical stress in the location of these components within suspensions, allow determining the value of the measurand vector. In case of capacitive sensors the sensitive elements

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(capacitors) at least partially are connected to the proof mass and move with the mass relative to the frame, which is mechanically connected to the other plates of the sensitive capacitors. Clearly it limits the freedom of proof mass movements and therefore the flexibility of designs, makes the mechanical microstructure very complex compared to Siantis approach and it makes a development of such sensors, as 6-axis sensors, very challenging, if not practically impossible. Siantis’ approach can be applied to different types of multi-axis sensors. If the proof mass is a structure exhibiting linear motion then the sensor can be a linear accelerometer, or inclinometer, or vibrometer. If the proof mass is a structure exhibiting angular motion then the sensor can be an angular accelerometer. If the proof mass is subjected to forced oscillations then the sensor can be an angular rate sensor (gyro). If the proof mass is an oscillating structure capable of an additional linear motion under acceleration then the sensor can be a 6-axis motion sensor. If instead of the proof mass an external force is used to load the microstructure then the sensor can be a three-axis force sensor. This patented technology for force sensors is being commercialized now for high volume application [7, 8]. Similar principle can be also applied to a magnetic field sensor. This unified approach builds the foundation for monolithic integration of different multi-axis sensors within one fabrication process.

5. Unified component platform It is well known that transistors both bipolar and CMOS can be used as mechanical stress sensitive components. It was also demonstrated that piezo-transistors can be fabricated within MEMS sensors, as was described above. Therefore, there are no limits for transistors to being used as both sensitive components and as signal processing components creating a unified component platform. This creates not only the convenience of components and processes standardization but also a basis for unified scaling of total micro-system, as the size of CMOS transistor scales down. As piezo-transistor area can be more than 1,000 times smaller than typical piezoresistor area, it immediately opens an opportunity to scale down the size of the sensor mechanical microstructure and springs, beams and other types of suspensions in particular. Figure 6 illustrates how the size of the beam connected to the frame in piezoresistive sensors can be decreased by switching to piezotransistors, as stress sensitive components. In typical layout of the piezoresistors, shown in Figure 6a, for a half-bridge circuit one of the p-type resistors should be longitudinal and another is transversal. It determines the minimal width of the beam for a chosen size of resistor. When piezo-transistors are used instead of piezoresistors, it allows decreasing the width of the beam, as multiple transistors would require much smaller area (Figure 6b). If requirements for the allowed deflection of the beam remain the same, then the length of the beam can also be decreased.

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(a)

(b)

Figure 6. Comparative geometries of the beams for piezoresistors (a) and piezo-transistors (b), as sensitive components.

Multiple sensitive components located in one area of the beam also allow measuring different stresses at this location: tensile, compressive, shear in different directions, which gives an additional advantage in measuring very complex mechanical motion of the proof mass relative to the frame of the sensor. It is important for the multi-axis measurements like 6-axis measurements.

6. Sensitive integrated circuits The general principle of sensitive integrated circuits technology is to combine large number of piezo-sensitive components for the purpose of increasing sensor sensitivity. In this case piezo-transistors are used not as active amplifying components but rather as three-port-pole components, which allows to combine more than four, like within Wheatstone bridge, components and by these means increase the signal-to-noise ratio. Without diving into the depth of this pending patenting technology let us illustrate this principle on the example of one specific sensitive integrated circuit based on bipolar piezo-transistors and piezoresistors shown in Figure 7 [9]. As can be seen from the circuit, only two three-port-pole sensitive components bipolar transistors allowed combining 10 piezo-sensitive components: two transistors and eight piezoresistors. While four piezoresistors, with about 1% relative resistance change in the working range, give output signal of about 1% of voltage supply, ten piezosensitive components of the above circuit gave 8.4% of voltage supply. Fabricated circuit pressure sensor for 40 KPa pressure range and 5 V voltage supply provided sensitivity 10.5 mV/KPa.

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Figure 7. Example of sensitive integrated circuit based on two bipolar piezo-transistors and eight piezoresistors.

Sensitive integrated circuits open the way of achieving dynamic range of these sensors about or greater than 106 with significant scaling sensor size down. One can imagine the unlimited hidden opportunities of this technology applied to CMOS circuitry. Differentiation of Siantis’ technology can be summarized as follows: Integration of CMOS with different sensors Smallest sensor area size shared with CMOS CMOS piezo-transistors as sensor components Circuit sensors Single simple microstructure for multi-axis measurements All the above open an opportunity in decreasing cost per sensor more than 10 times, higher sensitivity more than 100 times and higher reliability, which creates a strong foundation for a long-term roadmap of wide range of multi-sensor microsystems.

7. Economic justification of monolithic integration For the last 17 years the price per sensor axis decreased about 7 times, the same as for sensor size. Similar to IC in general, decrease of the die size is the major source of cost reduction. Today the lowest price for Accelerometers is about $0.4/axis and $1.5–2.5/axis for Gyro. Future individual sensor cost is predictable for currently employed technology and provides basis for sensors monolithic integration commercial rationale. As Sensor price decrease is exponential, it has become asymptotic – paradigm shift is required. Figure 8 illustrates some historical sensor die size decrease data. For the last 17 years the size of a sensor die has only decreased at the rate of 2X every 6.3 years (compared with CMOS rate of 2X every 1.5 years per Moore’s Law). Current average die size is around 1.3 mm2/axis for accelerometers

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and 10 mm2/axis for gyro. Best results, to our knowledge, are 0.8 mm2/axis for accelerometers (Hitachi) and 5 mm2/axis for gyro (Invensense). Future individual sensor die size (cost) is therefore predictable for currently employed technology. There are no reasons to believe that this rate will significantly change for the current technology – novel technology is required to improve this trend. For the same 17 years the size of a sensor microstructure was decreasing with the rate of 2X in every 17 years for accelerometers and 13 years for gyros. The size of the die was decreasing faster (2X/6.3 years) due to faster decreasing surrounding signal processing electronic circuits (ADI). Today micro-structure size is about 0.3–0.5 mm2/axis for accelerometers and about 3.5–5 mm2/axis for gyros. Future microstructure size (cost) is therefore predictable for currently employed technology. Siantis’ novel technology changes this paradigm.

Figure 8. Historical sensor die and sensor microstructure size decrease.

Estimating the IMU sensors cost for integration one can conclude that for a number of years ahead: expected price for 3-axis accelerometer will be in the range of $1–1.5; for 3-axis gyro – $3–4; for altimeter – $0.3–0.5; total cost (price) for a set of stand alone sensors will be therefore about $4–6. These prices ($1–1.5), ($3–4) and ($4–6) serve as benchmarks that determine the upper limits of the corresponding monolithic integration costs.

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The logistics of monolithic integration of sensors with CMOS might be describes as: 1. Monolithic Integration of CMOS with Sensors involves the following major additional expenses: cost of SOI initial material (~$800/wafer), cost of cap wafers (~$100/wafer), cost of MEMS processing (~$500/wafer). Total cost of monolithic integration ~$1,500/wafer. 2. Acceptance of this additional expense per wafer depends on the number of die per wafer. In turn, this depends on the die size, where these sensors are to be integrated. 3. Both sensor and CMOS costs reduce in concert with the die size reductions – effect on cost reduction is multiplied, as both are integrated on the same die. Large proof mass allows for stronger suspensions, which provides better reproducibility of sensor micro-structure geometry formed on SOI wafers. As a result, the yield loss related to fabrication of mechanical microstructures of sensors can be up to order of magnitude smaller than yield loss related to CMOS process. On the chart in Figure 9 the maximum allowable cost of monolithic integration per die, as a function of the die size is presented.

Figure 9. Maximum allowable cost of monolithic integration per die.

As can be seen from the chart, Siantis technology provides reduced cost even with large die sizes. Cost reduction improves dramatically with die size reduction and this is already part of CMOS roadmap. The size of the CMOS die, where monolithic integration can be justified today, should be smaller than about 7 × 7 mm for integration only with 3-axis accelerometer, smaller than 12 × 12 mm for integration only with 3-axis gyro and smaller than 15 × 15 mm for integration with 6-axis sensors. While the cost of

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monolithic integration (SOI wafers, MEMS processing, etc.) will be decreasing, the size of the CMOS dice, with which integration is needed, will also be decreasing along with the decreasing of the node size of CMOS. It will result in compounded savings on monolithically integrated products. One can make corrections to the above estimates of justified die size for monolithic integration by safeguarding the forecast of the corresponding stand alone sensors prices and cost of integration.

8. Conclusion Monolithic integration of CMOS with multiple sensors is inevitable. It provides clear path to lower cost and improved technical performance. However, current sensor technologies cannot support the required price point or process compatibility for monolithic CMOS integration. Siantis’ novel technology changes this paradigm by making monolithic integration of multiple different sensors with CMOS possible. Manufacturing costs are already lower than alternative schemes and there is a logical path to significantly reducing these costs further. These future cost reductions are realized in parallel with and due to decreasing size of CMOS transistors and provide a multiplication effect on the overall cost reduction achieved – far beyond what can be met by alternative approaches. Acknowledgments I would like to express my gratitude to Dr. Nickolai Belov, my colleague, partner and friend for many years who contributed to the development of Siantis’ technology and to some materials published in this paper.

References 1. 2. 3. 4. 5. 6. 7. 8. 9.

Kensall D. Wise, A revolution in information gathering, SmallTtimes, Nov/Dec, 2007. John Geen, David Krakauer, New iMEMS Angular-Rate-Sensing Gyroscope, Analog Dialogue 37-03 (2003). Michel Puech, Enabling DRIE processes for high potential MEMS products, Alcatel presentation, Santa Clara, Oct. 12, 2006. Roger T. Howe, Tsu-Jae King, Low-Temperature LPCVD MEMS Technologies, Mat. Res. Soc. Symp. Proc. Vol. 729, 2002. US Pat. 7367232, System and method for a three-axis MEMS accelerometer, (V.Vaganov, N. Belov), 2008. US Pat 7318349, Tree-axis integrated MEMS accelerometer, (V. Vaganov, N. Belov), 2008. US Pat 7476952, Semiconductor input control device, (V. Vaganov, N. Belov), 2009. US Pat 7554167, Three-dimensional analog input control device, (V. Vaganov), 2009. V.V.Beklemishev, V.I.Vaganov, V.V.Vorobjeva, IC pressure sensor based on piezoresistive circuits with bipolar piezotransistors and piezoresistors, Electronnaya Technika, 1980, series 10, #4, 78–85 (in Russian).

MEMS FOR PRACTICAL APPLICATIONS

MASAYOSHI ESASHI* Tohoku University WPI-AIMR, 6-6-01 Aza-Aoba Aramaki Aoba-ku Sendai, 980-8579, Japan

Abstract Silicon MEMS as electrostatically levitated rotational gyroscopes and 2D optical scanners, and wafer level packaged devices as integrated capacitive pressure sensors and MEMS switches are described. MEMS which use non-silicon materials as LTCC with electrical feedthrough, SiC and LiNbO3 for probe cards for wafer-level burn-in test, molds for glass press molding and SAW wireless passive sensors respectively are also described.

Keywords: MEMS, microphone, packaging, gyroscope, optical scanner, integrated sensor, pressure sensor, switch, probe card, LTCC, SiC, SAW (Surface Acoustic Wave), LiNbO3, transponder.

1. Introduction Micromachining is an extended IC fabrication technology based on deep etching, anodic bonding and other advanced process technologies. This is used to produce value added MEMS (Micro Electro Mechanical Systems) which have multifunctions in it. Examples of application oriented MEMS developed by open collaboration with industry are described below.

2. Silicon MEMS 2.1. MEMS MICROPHONE Capacitive MEMS microphone developed in NHK Science & Technology Research Laboratories [http://www.nhk.or.jp/strl/english/index.html] is shown in Figure 1 [1]. The displacement of the diaphragm by the sound pressure is capacitively detected. The MEMS microphone has been used for TV programs.

______ * Masayoshi Esashi, Fax +81-22-795-6935, E-mail: [email protected]

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Figure 1. Capacitive MEMS microphone.

2.2. ELECTROSTATICALLY LEVITATED ROTATIONAL GYROSCOPE Silicon rotational gyroscopes have been developed for the purpose of motion control and navigation [2]. The principle and the photograph are shown in Figure 2. A 1.5 mm diameter silicon ring which is electrostatically levitated by a digital control using a capacitive position sensing and an electrostatic actuation is rotated at 74,000 rpm. The rotation is based on the principle of a variable capacitance motor. A 5 μm radial gap between the ring rotor and stator electrodes is formed using deep RIE (Reactive Ion Etching) of a silicon wafer. The silicon is anodically bonded on both sides to glasses which have electrodes. The chip is packaged in a vacuum cavity to prevent a viscous damping. This inertia measurement system (Tokyo Keiki Inc. [http://www.tokyo-keiki.co.jp/e/index.html] MESAG (Micro Electrostatically Suspended Accelerometer Gyro)) can measure two axes rotation and three axes acceleration simultaneously with high precision (sensitivity 0.01°/s and 0.2 mG respectively).

Figure 2. Electrostatically levitated rotational gyroscope.

2.3. TWO DIMENSIONAL OPTICAL SCANNER Electromagnetic 2D (two dimensional) optical scanners as shown in Figure 3 were developed [3]. A mirror is deflected electromagnetically using planer coils on a silicon gimbal structure and external permanent magnets. The scanner (Nippon

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Signal Co. Ltd.[http://www.signal.co.jp/english/], ECO Scan) has been applied to a 3D imaging system by measuring the distance to the object using a time-of-flight of a laser light as shown in Figure 3.

Figure 3. 2D optical scanner and its application to a time-of-flight 3D imaging system.

3. Wafer level packaging Packaged chip-size MEMS are fabricated by the anodic bonding of a silicon wafer and a glass wafer and by dicing the bonded wafer to chips. This process called wafer level packaging is effective for surface mounting and a small volume production because it makes batch assembly of small sized devices possible and hence automated machines to assemble each chip can be eliminated [4]. The method has advantages of reduced test cost and high reliability. Electrical feedthrough from the glass hole plays important roles for the wafer level packaging. 3.1. CAPACITIVE PRESSURE SENSORS The fabrication process of an integrated capacitive pressure sensor [5] is shown in Figure 4. The silicon is used not only for a capacitive diaphragm pressure sensor and a CMOS capacitance detection circuit, but also a package. The integrated capacitive pressure sensor has been produced in JTECT Corp. [https: //www.hmisource.com/otasuke/files/manual/gpproex/v2_21/device/toy.htm] and used for low pressure measurement. Using the wafer level packaging a capacitive vacuum sensor which has a thin diaphragm and a reference vacuum cavity incorporating a getter in it has been produced by Canon Anelva Corp. [http://www.canon-anelva.co.jp/english/index.html] (Figure 5) [6]. The getter is needed to absorb an oxygen gas generated electrochemically at the glass–silicon interface during the anodic bonding process.

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Figure 4. Fabrication process of an integrated capacitive pressure sensor.

Figure 5. Capacitive vacuum sensor.

3.2. MEMS SWITCH MEMS switch which uses a thermal bimetal actuator for making electrical contacts was developed [7] (Figure 6). The electrical connections are made to the backside using the electrical feedthrough in a glass. The wafer level packaging

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results in not only low cost fabrication but also excellent reliability because the contact surface is kept contamination-free owing to the hermetic sealing. Operations more than 107 cycles and a high frequency response up to 20 GHz were achieved. This switch has been produced and used for latest high speed LSI testers by Advantest Corp.[http://www.advantest.com/].

Figure 6. MEMS switch.

4. MEMS with non-silicon materials 4.1. PROVE CARD FOR WAFER-LEVEL BURN-IN TEST (LOW THERMAL EXPANSION COEFFICIENT LTCC) Electrical feedthroughs made in LTCC (Low Temperature Co-fired Ceramics) was developed in Nikko Inc.[http://www.nikko-company.co.jp/] [8]. As shown in Figure 7, the through holes are made by puncturing the soft green sheet and the holes are filled with a gold paste. The sheet is sintered to make a ceramic, in which process the lateral dimension can be controlled by sintering under pressure. This LTCC wafer can be anodically bonded to a silicon wafer to be used for the wafer level packaging. A multilayered ceramic wafer is fabricated by laminating the green sheets before sintering. The photograph of the cross section of the laminated LTCC with feedthrough is shown in Figure 5. The thermal expansion of the LTCC is matched with silicon. The LTCC with feedthrough was applied to MEMS probe cards [9]. The fabrication process and a photograph are shown in Figure 8. Nickel probes are made by electroplating nickel into a silicon mold and then soldered to the LTCC wafer with AuSn. Finally the silicon mold is etched out. The probe card has similar thermal expansion with silicon, which makes for wafer level burn-in test (reliability test at an elevated temperature on a wafer) possible.

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Figure 7. Fabrication process and cross-section of LTCC with the electrical feedthrough.

Figure 8. Fabrication process and a photograph of probe card for a wafer-level burn-in test.

4.2. SiC MICROSTRUCTURE FOR GLASS PRESS MOLDING (SiC) SiC (silicon carbide) microstructure can be used as a mold to form glass parts by pressing. This takes advantages of the hardness of the SiC at high temperature. The fabrication process is shown in Figure 9a [10]. The SiC was deposited on a

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micromachined silicon wafer by CVD. The SiC surface is ground and bonded to a SiC ceramic plate by a reaction bonding using an interfacial nickel film. Finally the silicon wafer is etched away. The micromachined silicon wafer which has a surface profile for non-spherical lens was made by transferring the resist profile using the RIE. The resist profile was made by a mask less multiple exposure system using the DMD (Digital Micro mirror Device) [11]. The photographs of the SiC mold for a lens and the Pyrex glass press formed are shown in Figure 9b, c respectively.

(a) Fabrication process

(b) SiC mold

(c) Pyrex glass fabricated by mold press

Figure 9. SiC microstructure for glass press molding.

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(a) Principle

(b) Structure

(c) Experimental results Figure 10. SAW passive wireless sensor for pressure measurement.

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Figure 11. Fabrication process of the SAW passive wireless pressure sensor and the photograph of the cross section.

4.3. SAW PASSIVE WIRELESS SENSOR (LiNbO3) 2.45 GHz SAW (Surface Acoustic Wave) based passive transponders for wireless sensing have been developed. The principle and the photograph are shown in Figure 10a. Receiving the 2.45 GHz electromagnetic wave, a surface acoustic wave generated by the IDE (Inter Digital Transducer) on a LiNbO3 substrate propagates.

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It is reflected and a 2.45 GHz electromagnetic wave is transmitted back and the sensing can be performed by measuring the delay time. The structure and the experimental result of the pressure sensor are shown in Figure 10b, c. The delay time is modulated by the deformation of the diaphragm by the pressure. Temperature can be also measured from the temperature dependency of the delay time and multiple reflectors are formed for the temperature compensation in the pressure measurement. The SAW pressure sensor was developed for the TPMS (Tire Pressure Measurement System) [12]. The fabrication process of the TPMS is shown in Figure 11. A thermal inversion of polarization and a polarization dependent selective etching of LiNbO3 are used for the fabrication [13].

5. Conclusions MEMS play important roles as key devices in various systems. Packaging and electrical interconnection are needed for small sized and high reliability MEMS. Not only silicon but also other materials such as LTCC, silicon carbide and LiNbO3 could be used effectively for MEMS.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

T.Tajima. et. al.: Microelectronic Engineering, 67–68, 508–519 (2003) T.Murakoshi et. al.: Jpn. J. Appl. Phys. 42, 2468–2472 (2003). N.Asada. et.al.: IEEE Trans. on Magnetics 30, 4647–4649 (1994). M.Esashi.: Microsystem Technologies, 1, 2–9 (1994). Y.Matsumoto and M.Esashi: Electronics and Communications in Japan, 76, 93–106 (1992). H.Miyashita and Y.Kitamura: Anelva Technical Report, 11, 37–40. (2005) (in Japanese). A.Nakamura et. al.: Advantest Technical Report,.22, 9–18 (2004) (in Japanese). M.Mohri.et.al.: 23th Convention of Japan Inst. of Electronic Packaging, 51–52 (2009). (in Japanese). S.-H.Choe.et. al.: IEEE International Test Conference 2007, 20.2, (2007). K.O.Min et. al.: Proc. of the 21th Sensor Symposium, 473–478 (2004). K.Totsu.and M.Esashi.: J. Vac.Sci.Technol., B23, 1487–1490 (2005). S.Hashimoto et. al.: Proceedings of the 24th Sensor Symposium, 267–271 (2007). A.B.Randles et. al.: Proc. 2008 IEEE International Ultrasonic Symposium, 1124–1127 (2008).

NANOCHIP: A MEMS-BASED ULTRA-HIGH DATA DENSITY MEMORY DEVICE

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NICKOLAI BELOV , DONALD ADAMS , PETER ASCANIO , TSUNG-KUAN CHOU 2 , JOHN HECK2 , BYONG KIM 1 , GORDON KNIGHT 1, QING MA2 , JONG-SEUNG PARK1 , VALLURI RAO2 , ROBERT STARK1 , AND GHASSAN TCHELEPI 1

1 Nanochip, Inc., 48041 Fremont Blvd., Fremont, CA, 94538, USA, E-mail: [email protected] 2 Intel Corporation, 2200 Mission Blvd., Santa Clara, CA, 95054, USA, E-mail: [email protected]

Abstract The paper provides an overview of a probe storage device development. The main results are related to successful development of ferroelectric memory, MEMS micro-mover with large range of motion and an array of cantilevers with sharp tips (read–write heads), demonstrating wear resistance of the tips, integration of memory material into the MEMS process, integration of MEMS cantilever process with CMOS, development of analog front end electronics, including read channel and servo system, and a controller for a storage device.

Keywords: Probe storage, non-volatile memory, ferroelectric memory, scanning probe charge reading, MEMS, CMOS-MEMS integration, micro-mover.

1. Introduction Although development of a probe storage device is linked to a wide spectrum of technical tasks, which should be solved in order to demonstrate viability of the technology, the main development areas are: • • •

Memory material and read–write methods MEMS, including X–Y micro-mover and large array of read–write heads Electronics and system engineering Requirements for the probe storage devices include: (a) memory solution suitable for storing small bits (20–30 nm) with acceptable retention, providing at least 16–32 GB capacity and offering a clear roadmap for at least next three generations; (b) robust read–write method making feasible data transfer rate of at least 20 MB/s with a reasonably small number of read–write channels; (c) MEMS-based X–Y scanner suitable for high-volume manufacturing and featuring a large range of motion, accurate position sensing and good shock protection; (d) large arrays E. Gusev et al. (eds.), Advanced Materials and Technologies for Micro/Nano-Devices, Sensors and Actuators, DOI 10.1007/978-90-481-3807-4_4, © Springer Science + Business Media B.V. 2010

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of AFM-type sharp tips (10–50 nm) working as read–write heads and having built-in actuation to allow engagement of selected heads with memory material; (e) production-friendly and cost-effective integration of memory material, MEMS and electronics in one device, including wafer-level or die-level assembly process that combines components fabricated on different substrates; (f) tribology solution providing required longevity to the read–write heads; (g) system solution for electronics, including read–write channel, data management electronics, servo system for X–Y scanner and standard interface; and (h) processing digital data stream under conditions typical for target applications. Meeting all performance, cost, and reliability requirements, which would allow for successful competition with existing storage devices, represents another layer of work related to product development and commercialization of the technology. Design and fabrication of prototypes of probe storage devices and/or components for them was addressed previously by several companies. There are more than 100 papers and patents on development of a probe storage device called Millipede at IBM [1–2]. The team at IBM achieved excellent results and demonstrated a prototype of probe storage device meeting many of the above requirements. Millipede utilizes a polymer-based storage medium. Writing bits is done by making indentations in the polymer by thermally-actuated cantilevers with sharp tips. Reading is based on thermal sensing, which allows for distinguishing the cases of tip facing a surface of polymer with and without indentation. Slow writing, high power consumption, high temperature sensitivity and difficulties with erasing/overwriting the data are the major drawbacks of this approach. Several other companies including Hewlett–Packard, Seagate, Samsung, Intel, ST Microelectronics and Hitachi filed multiple patent applications [3–8] related to both components of probe storage devices – memory, X–Y micro-movers, probes and methods of writing and reading the data. No publications on prototypes of the probe storage devices fabricated by these companies are available. Nanochip has developed a prototype of probe storage device (nanochip) utilizing ferroelectric memory.

2. Memory material and read–write–erase operations Nanochip uses a ferroelectric non-volatile memory for probe storage application. The ferroelectric memory material permits robust write (electric field switching), non-destructive read (charge detection) and simple overwriting (non-return-to zero process) of data bits with adequately long retention (>1 year), many R/W cycling (>200k), and good tip/media wear (~5 km at speed of 1 cm/s) performance. Ferroelectric recording medium uses a layer of ferroelectric material placed between two electrodes. An electric field created between the electrodes forces the domain polarization to be parallel to the applied field. For probe storage application, a conductive tip is a top electrode, while a conductive layer under the ferroelectric medium serves as a bottom electrode. A voltage applied between the tip and the bottom electrode creates a local electric field across the medium and allows for switching a domain polarization in a ferroelectric material to an UP or DOWN state and this can be equivalent to digital information of 1 or 0.

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A triple stack of epitaxial perovskite oxide layers (PZT/SRO/STO) grown on Si wafers was used as a memory (memory stack). PZT is the ferroelectric recording media. SRO serves as the bottom electrode. STO is a dielectric film serving as the buffer layer formed on the Si wafer that facilitates the single crystalline growth of SRO and PZT. Thickness of the layers is in a range of 20–100 nm. The stack is deposited using a combination of thin film growth techniques: metal-organic chemical vapor deposition, sputtering, and molecular beam epitaxy. The PZT is atomically smooth with the surface RMS roughness between 0.2 and 0.7 nm (as measured by atomic force microscopy). X-ray diffraction analysis shows that the PZT is formed of tetragonal perovskite lattice structure comprising 180° polarization domain. The background polarization of a freshly as-grown PZT is poled naturally to an UP state (as characterized by piezoresponse force microscopy (PFM) [9]). 2.1. WRITE OPERATION Writing of ferroelectric domains of alternating polarity in a PZT media using a train of voltage pulses applied to a probe tip was used for characterization of write operation capabilities. The tip moves in contact with the media surface at the velocity synchronized with the pulse train frequency to write an array of alternating polarization domains (bits) of desired pattern wavelength. Well-defined and uniform bits array can be readily written in this way. The array of bits as small as 19 nm in diameter and spaced by 19 nm have been written [10] with probe tip scanning at the high speeds of 0.1–1cm/s and biased with nanoseconds to microseconds range voltage pulses. Such scanning speed writing process translates to the recording data rates in a range of 0.1–1 Mbps per tip. In Figure 1, overwriting capability in ferroelectric probe storage is demonstrated for the first time using a probe tip scanning with a relatively high speed (~1 mm/s in the x-axis direction in Figure 1) and biased with a bipolar non-return-to-zero voltage write process. Typical track width (i.e., vertical dimension of the bits in Figure 1) is ~40 nm. The write process shows writing first pattern (a), adding two additional writes of small bits offset from old tracks (b), erasing media (c), and writing small dots after erase (d). PFM was used to read out the bits images in Figure 1 which measures a 4 × 4 μm scan area individually. 2.2. READ OPERATION Nanochip developed a scanning probe charge reading technique (SPCRT) to provide a high speed bit reading method compatible with MEMS and CMOS device integration. In SPCRT [11], a conductive probe tip connected with a charge-amplifier circuitry is used to detect a polarization bit signal like the bit signal trace demonstrated in Figure 2a. The charge-amp coupled tip scans the surface of PZT written with the bit array with high speeds (0.1–1 cm/s) and detects the bit signal with the data rate in a range of a 1 k–1 Mbps per tip. The bit signal trace of Figure 2a corresponds to three wavelength alternating polarization domains; 6 cycles of 0.9 μm wavelength bits, 9 cycles of 0.6 μm wavelength bits,

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and 12 cycles of 0.4 μm wavelength bits formed by applying a bipolar non-returnto-zero voltage pulse train. Figure 2b is an amplitude signal trace of the same three wavelength bits readout using PFM. Both SPCRT and PFM techniques resolve all of the three wavelength bits well. The SPCRT have shown to read the individual bits for numerous cycles (>100k times). It is noted that a variant version of SPCRT called “M-SPCRT” that takes advantage of a lock-in technique has also been developed to read ferroelectric bit charge signals on PZT with nanoscale spatial resolution [10].

Figure 1. PFM images of bits at various “writing” stages.

Figure 2. Signal trace of three wavelength bits: (a) SPCRT and (b) PFM.

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2.3. RETENTION AND ENDURANCE CYCLING Figure 3a shows small inverted dots (diameter 28 nm on average) imaged by PFM within an hour after they are first written. The dots are shown with brighter contrast. A train of 150 ns voltage pulsing to the tip sliding with the speed of 1.3 mm/s was used to write the dots array with the writing data rate ~41 kbps. Figure 3b shows the PFM image of the dots 68 h after Figure 3a was taken. The time comparison of the dots show good retention under the room ambient condition over a period of few days tracked. A temperature accelerated retention test on similar type of dots confirmed that the small dots can stay with over a year of retention. It is our general learning that small inverted UP-polarization dots when formed over a DOWN polarization background can remain with retention much better than inverted dots formed over an UP-polarization background. Cycling of writing, easing, overwriting, and reading per same bit spot has been tested. Figure 4 is a plot of bit polarity readout by PFM as a function of number of writing/erasing/overwriting cycles completed before reading bits. Solid-triangle or solid-circle respectively refers to PFM phase signal of an UP or DOWN bit after cycling. It is shown that the bits can be rewritable with better than 200k endurance

(a) ~28 nm bits at t = 0 h after writing.

(b) ~28 nm bits at t = 68 h.

Figure 3. PFM reading of bits at different times in room ambient condition.

Figure 4. Cycling test of writing, easing, overwriting, and reading by PFM.

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cycling. The cycling was conducted using 10 μs bipolar voltage pulses with 1 μs delay. It is noted that topography generation during cycling of PZT is a cycling failure mode. Under a controlled condition (in terms of surface and environmental cleanness), topography can be reduced adequately to yield with the 200k cycles. The topography generation is also voltage-dependent and can be significantly reduced with unipolar pulsing (vs. bipolar pulsing). 2.4. WEAR Tip/media wear is an important parameter to be kept under control from the bit capacity and size, and data rate improvement perspectives. In general smaller and higher density bits can be written and read when tips are made shaper and/or media is smoother. Data rate is largely a function of scan speed that a tip slides over the media surface. The contact force should not drift much, especially when the tip moves with high speed to reduce tip/media wear. Once high density and high data rate can be achieved by engineering, tip/media wear needs to be kept to minimum to preserve the high performance R/W. Nanochip found a way to maintain the tip/media wear to functional level even when the tip is traveled over the media for a distance of few kilometers with a 1 cm/s scanning speed. In Figure 5, a tip was able to write a 25 nm dot after scanning in contact with a PZT media for ~5 km with a speed of 1 cm/s. The tip was loaded with the normal force 106 Ωcm), 2 μm thin GaAs layer, was deposited. The growth experiments were performed in a VG80 horizontal MBE chamber with a background pressure of 10–10 mbar. During growth, the chamber pressure was 10–7 mbar. The MBE layer structure is shown in Figure 1.

Figure 1. The MBE layer structure used in filter and antenna manufacturing.

Conventional contact lithography, e-gun evaporation and lift-off techniques were used to define the filter structure. A 500 Å Ti/7000 Å Au metallization was used, then the wafers were mounted face-down on special glass plates and the GaAs substrate was thinned down to 150 μm by lapping technique.

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The etching pattern for the membranes was defined by backside alignment contact photolithography. The membranes were fabricated in a Vacutec 1350 Reactive Ion Etching (RIE) chamber using CCl2F2. End point detection and optical (visual) detection was used during the RIE process. After the selective etching, the thickness of the membrane is about 2.2 μm. A SEM photo of the GaAs membrane (after RIE) used as support for the filter structure is presented in Figure 2. A top photo of the GaAs membrane supported coupled line filter is presented in Figure 3. The results of S parameter measurements are presented in Figure 4. Losses smaller then 0.9 dB were obtained. The very good performances obtained for the 35 GHz filter structures together with the results obtained for the 45 GHz filter structure [15] demonstrate the capability of micromachining technologies of GaAs, the reliability of the structures and the possibility to obtain high performance millimetre wave circuits using GaAs MEMS type devices.

Figure 2. SEM photo of the GaA membrane used as support for the filter and antennae structures; the profile of the etched walls obtained by dry etching is visible.

Figure 3. GaAs membrane supported coupled line filter – top photo.

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Figure 4. S parameter measurements for the micromachined coupled line filter for 35 GHz. Losses as low as 0.8 dB have been obtained.

3. GaAs membrane supported Yagi–Uda antennae First membrane supported antennas were proposed by Rebeiz et al. [19]. The antenna was a dipole, suspended in an etched pyramidal cavity on a 1 µm silicon oxi-nitride membrane. Micromachined microstrip antennas were first presented in [20, 21]. One solution for many millimeter wave applications is the use of the double-folded slot antenna. First micromachined folded slot antennae were developed by Neculoiu et al. [22]. All these structures were broadside –type antennae (the radiation pattern is perpendicular to the antenna plane). Endfire antennae have the radiation pattern along the plane of the antenna structure. For the millimeter wave range recent studies [23, 24] have demonstrated that the Yagi–Uda configuration is a very good solution for millimeter-wave frequencies and above. The Yagi–Uda endfire antenna is a traveling-wave structure that, as the number of elements increases, has improved directivity, gain and frontto-back ratio. Using micromachining techniques it is possible to fabricate Yagi– Uda antennae on a very thin dielectric membrane. The overall dimensions of the antenna are comparable with the free space wavelength, so this approach is very well suited for millimeter -wave and sub-millimeter-wave frequency range, up to the terahertz region. Using the Zeland IE3D software the Yagi–Uda antenna was designed by optimization of the layout dimensions (driver, directors and reflector parameters, in terms of spacing, length and width). The main target parameter was the antenna gain, which is in close connection with the antenna reflection losses and the radiation pattern. Antenna gain must be maintained at reasonable values across the entire operating bandwidth centered on 45 GHz. The final optimization of the antenna layout includes the CPW-slotline transition parameters (the length of the slots, the length of the slotline, etc.).

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Similar MBE grown wafers like for the filter structures have been used. The major difference in the technology was determined by the idea to obtain a so called “three edges membrane” supporting the end-fire antenna structure. The bulk GaAs wall surrounding the membrane supported antenna on the four edges structure was removed on one edge, in the main radiation direction of the antenna. This topology creates optimum propagation conditions. Conventional contact lithography, e-gun evaporation and lift-off techniques were used to define the antenna structure. A 500 Å Ti/7000 Å Au metallization was used. Then, a front side wet etching was employed in order to define the periphery of the antenna chip and also to locally remove the AlGaAs etch stop layer. Then the same procedure, used for the backside processing for used for the filters was employed for the antenna structures. Due to the local removal of the AlGaAs etch stop layer, the antenna chips are individually formed in the RIE chamber. Top and bottom photos of the antenna structures mounted on the PBC are presented in Figure 5.

Figure 5. Top (left) and bottom (right) view of the membrane supported Yagi–Uda antenna for 45 GHz mounted on the printing board.

Figure 6. Return losses vs frequency for 60 GHz Yagi–Uda antenna.

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The microwave measurements were performed using an “on wafer” measuring set-up equipped with Cascade Microtech coplanar probes and a Vector Network Analyzer. The antennae chips were placed on an empty plastic box to assure the almost free space conditions. Gain measurements were performed by “on wafer” measurements using a method developed in [25]. The measured gain was about 6.7 dBi at 60 GHz (the simulated value was 7.5 dBi). The agreement between the predicted and measured resonance frequencies is very good for the 60 GHz antenna (Figure 6).

4. Monolithic Integration of a Schottky diode with a Yagi–Uda antenna on the same GaAs membrane GaAs micromachining is very interesting due to the easy monolithic integration of micromachined passive circuit elements with active devices manufactured on the same chip. The monolithic integration of a membrane-supported antenna with a detecting Schottky diode is a practical solution for building very compact and lowcost receivers for the millimetre and sub-millimetre wave frequency range. We will describe results obtained with the monolithic integration of a membrane supported Yagi–Uda antenna with a “membrane” Schottky diode. These devices were integrated on the same 2.2 µm thin GaAs membrane in a direct (video-type) receiver structure. The design approach of the receiver front-end splits the circuit into the membrane supported circuit block (micromachined antenna monolithically integrated with the millimeter-wave Schottky diode) and the bulk GaAs supported circuit block (low-pass filter for video output). Each block is modelled and designed using the full-wave electromagnetic (EM) simulation software Zeland IE3D. The MBE structure used in the manufacturing of the receiver structure is presented in Figure 7. An eight mask process, to manufacture the receiver structures, was developed. The first two masks are the mesa masks, which define the diode. There are squares

Figure 7. The MBE heterostructure used for the receiver manufacturing.

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with the side of 36 µm and respectively 10 µm. The second square is centered in the first. It follows the mask which defines the ohmic metallization which has to reach over the big mesa in one margin and to define the antenna. Rapid thermally annealed ([Au/Ge]×4/Ni/Au – with a total thickness of 0.2 μm) is used for the ohmic contact formation. In order to obtain an 1 µm thin gold layer, it is necessary to use an overlay mask which is used to lift-off the gold over the ohmic contact. The fifth mask defines the poliymide necessary to avoid the short-circuit between the future Schottky contact with the big mesa (a “polyimide bridge” will be created). The sixth mask is used to define the Schottky metallization performed by lift-off technique and is the most critical process. The dimensions of the Schottky contacts on the mask are 3.5 µm × 3.5 µm. The seventh mask is used to define the receiver structures on the top and to make possible to achieve a “three edges” topology by a short etching from the top. The last mask is the membrane mask which is used to define the membranes from the bottom of the wafer. Selective RIE process with CCl2F2 and end point and optical detection were used for the formation of the membrane.

Figure 8. Photo of a GaAs wafer containing monolithic integrated receiver structures with the Yagi–Uda antenna and the Schottky diode supported on the same 2.2 μm thin GaAs membrane.

A top photo of the receiver structure is presented in Figure 8. An optical photo of the Schottky diode region, including the polyimide-bridge (the Schottky diode is placed in the feeding point of the antenna-between the drivers’ arms) is presented in Figure 9. The diode parameters were extracted from the I–V measurements and also from microwave measurements of test structures placed on the same chip with the receiver structure (Figure 9). We have determined IS = 10–13–10–12 A; the ideality factor n = 1.24–1.27; the series resistance Rs = 15–20 ohm, the zero-voltage junction capacitance Cjo = 10–20 fF; junction potential Vj = 0.7–0.85 V. The

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receiver front-end was measured using the Yagi–Uda antenna from the previous section as an emitter. The antenna was feed with microwave signal from a millimeterwave power generator via on wafer probe tips. The amplitude-modulated signal was emitted into free-space, was captured by the receiver antenna and was detected by the diode. An oscilloscope displayed the video signal.

Figure 9. Detail with the membrane supported Schottky diode area. The diode is placed between the two drivers of the antenna.

Figure 10. Experimental set-up for receiver characterization.

The experimental characterization of the Yagi–Uda antenna receiver was performed using the measuring set-up presented in Figure 10 [9]. A standard V-band horn antenna was placed in the same plane with the receiver structure in far field conditions. The antenna was connected to an amplitude modulated millimeter-wave signal generator and operated as an emitter. The modulation frequency was set to 1 kHz. The receiver structure collects the signal and detects the low frequency component that is amplified by a low-noise video amplifier and then displayed using a digital oscilloscope. The gain of the video amplifier was about 10 and the bandwidth was between 10 Hz and 10 kHz. The generator power was 20 dBm and the distance between the horn antenna and the receiver structure was set to 153 mm.

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The measured detected voltage as a function of frequency for a constant bias current of 10 µA is presented in Figure 11. The membrane-supported Yagi–Uda antenna receiver radiation pattern of was measured for the first time in an anechoic room. In this case it was not possible to use a amplitude modulated millimeter-wave signal, so only the DC detected signal was used. As an effect, the dynamic range of the measured detected voltage was limited to about 20 dB. The results were normalized to the maximum value. The operating frequency was 60 GHz. The E-plane radiation pattern is presented in Figure 12 (E-plane is the plane that contain the receiver metallization). Using this receiver structure, the very exciting concept of millimetre wave identification (MMID) was demonstrated [26]. There are several advantages of

Figure 11. Experimental detected voltage as a function of frequency at constant bias current.

Figure 12. Experimental E-plane normalized radiation pattern (linear scale, normalized to maximum values).

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MMID over RFID. At millimeter waves, e.g., 60 GHz, high data-rate communications with even gigabit data rates can be implemented. An interesting application would be batteryless wireless mass memories that can be read in a few seconds with high data rates. Furthermore, at millimeter waves, directive antennas are small. A reader device with a small directive antenna would provide the possibility of selecting a transponder by pointing toward it. This is not possible in today’s UHF RFID systems because directive antennas are too large. A directive reader antenna would help in locating transponders in high-density sensor networks or other places where transponders are densely located, e.g., in item level tagging. Finally, there are already applications where millimeter-wave radars are used, as in automotive radars. These radars could, in principle, be used as MMID reader devices that could communicate with the transponders. Imagine a transponder in a child’s clothing that gives a warning to oncoming cars, thus preventing a fatal accident. These receiver structures demonstrate the capabilities of micromachining technologies of compound semiconductors, to integrate passive and active circuit elements in complex millimeter wave circuits. This is very important especially when frequency increases, in the submillimeter or THz range and other technologies and materials can not be used.

5. Conclusions This paper has presented some new results regarding the design manufacturing and characterization of GaAs membrane supported millimetre wave circuits (filters, antennae and monolithic integrated receiver structures). The very good results have demonstrate the possibilities of GaAs micromachining technologies in manufacturing of high performance circuits. These types of circuits are devoted to emerging communication systems, operating in the millimetre and sub-millimetre frequency range. Acknowledgments The authors acknowledge the support of the European Commission through the FP6 European Project 507352 “AMICOM”. The Romanian authors also acknowledge the support of the European Commission through the FP7 European project 202897 “MIMOMEMS” and to the Romanian Agency for Research and Inovation through the projects MIMFOMEMS and GIGASABAR.

References 1.

Weller TM, Rebeiz GM and Katehi LP (1993) Experimental results on microshield transmission line circuits. IEEE-MTT-S International Simposium Digest 2:827–830.

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A. MÜLLER ET AL. Drayton RF, Katehi LP (1992) Development of miniature microwave circuit components using micromachining techniques. IEEE-MTT-S International Simposium Digest 1:225– 228. Drayton RF, Katehi LP (1995) Development of self-packaged high frequency circuits using micromschining techniques. IEEE Trans. on MTT 43:2073–2080. Katehi LP, Rebeiz GM (1996) Novel micromachined approaches to MMIC’s using lowparasitic, high performance transmission media and environments. IEEE MTT-S Digest: 1145. Müller A, Konstantinidis G, Giaccomozzi F, Lagadas M, Deligeorgis G, Iordanescu S, Petrini I, Vasilache D, Marcelli R, Bartolucci G, Neculoiu D, Buiculescu C, Blondy P, Dascalu D (2001) Micromachined filters for 38 and 77 GHz supported on thin membranes. J. Micromech. Microeng. 11:1–5. Konstantinidis G et al. (2001) MEMS Components and Applications for Industry, Automobiles, Aerospaces and Communication. Proceeding of SPIE 4559:157–161. Siegel PH, Smith RP, Martin S, Gaidans M (1999) 2.5-THz GaAs Monolithic MembraneDiode Mixer. IEEE, Trans. Microwave Theory Tech, 47: 596–604. Ichizli V, Rodriguez-Girones M, Lin CI, Szeliga P and Hartnagel HL (2001) The Effect of Gas Plasma on the Deposition Quality of Schottky Metals and Interconnect Metallisation for Planar Diodes Structure for THz Applications. 9TH Intern. Conf. on THz Electronics, Charlottesville, Virginia. Konstantinidis G, Neculoiu D, Lagadas M, Deligiorgis G, Vasilache D and Müller A (2003) GaAs membrane supported millimeter wave receiver structures. J. Micromech. Microeng. 13:353–358. Neculoiu D, Müller A, Konstantinidis G (2006) Electromagnetic modelling of GaAs membrane supported mm-wave receivers. Journal of Physics: Conference Series 34:28–33. Siegel PH (2002) Terahertz technology. IEEE Trans on MTT 50:910–928. Chi CY, Rebeiz GM (1995) Planar microwave and millimeter-wave lumped elements and coupled-line filters using micro-machining techniques. IEEE Trans on MTT 43:730–738. Blondy P, Brown A, Cross D, Rebeiz GM (1998) Low- Loss Micromachined Filters for Millimeter Wave Communications Systems. IEEE Trans. on MTT 46: 2283–2288. Neculoiu D, Bartolucci G, Pons P, Bary L, Vasilache D, Buiculescu C, Vladoianu F, Dragoman M, Petrini I, Müller A and Plana R (2003) Low-losses coupled-lines silicon micromachined band-pass filters for the 45 GHz frequency band. Proc of the IEEE International Semiconductor Conference CAS 2003 1:109–112. Pantazis A, Neculoiu D, Hazoupulos Z, Vasilache D, Lagadas M, Dragoman M, Buiculescu C, Petrini I, Müller A A, Konstantinidis G, Müller A (2005) Millimeter-wave passive circuit elements based on GaAs micromachining. Journal of Micromech. Microeng., 15:S53–S59. Bartolucci G, Neculoiu D, Dragoman M, Giacomozzi F, Marcelli R, Muller A (2003) Modeling, Design and Realisation of Micromachined Millimeter Wave Band-pass Filters. Int. Journal of Circuit Theory and Applications 31:529–539. Neculoiu D, Bartolucci G, Pons P, Bary L, Vasilache D, Müller A and Plana R (2004) Compact membrane-supported bandpass filter for millimeter-wave applications. Electronics Letters 40:180–182. IE3D User’s Manual, Release 14, Zeland Software Inc., Freemont, CA, 2008. Rebeiz GM, Kasilingam DP, Guo Y, Stimson PA, Rutledge DB (1990) Monilithic Millimeter-Wave Two-Dimensional Horn Imaging Arrays. IEEE Trans. on AP 38:1473– 1482. Gauthier GP, Courtay A, Rebeiz GM (1997) Microstrip Antennae on Synthesized Low Dielectric-Constant Substrates. IEEE Trans. on AP 45:1310–1314. Gauthier GP, Raskin JP, Katehi LP, Rebeiz GM (1999) A 94-GHz Aperture-Coupled Micromachined Microstrip Antenna. IEEE Trans. on AP 47:1761–1766.

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22. Neculoiu D, Pons P, Plana R, Blondy P, Müller A, Vasilache D (2001) MEMS antennae for millimeter wave applications. Proceeding of SPIE, San Francisco 4559:66–73. 23. Neculoiu D, Pons P, Vasilache D, Bary L, Müller A, Plana R (2003) Membrane-supported Yagi–Uda Antennae for Millimeter-Wave Applications. Proceeding of 3rd ESA Workshop, Espoo, Finland, 1:603–608. 24. Müller A, Saadaoui M, Pons P, Bary L, D.Neculoiu, Giacomozzi F, Dubuc D, Grenier K, Vasilache D and Plana R (2003) Fabrication of silicon based micromachined antennae for millimeter-wave application. Proc of MEMSWAVE workshop, Toulouse, 1:D15–18. 25. Neculoiu D, Pons P, Bary L, Saadaoui M, Vasilache D, Grenier K, Dubuc D, Müller A and Plana R (2004) Membrane Supported Yagi–Uda Antennae for Millimeter-Wave Applications. IEE Proc. on Microwave, Antennas and Propagation 151:11–314. 26. Pursula P, Vähä-Heikkilä T, Müller A, Neculoiu D, Konstantinidis G, Oja A and Tuovinen J (2008) Millimetre Wave Identification — A new short range radio system for low power, high data rate applications. IEEE Trans on MTT 56:2221–2228.

MONOCRYSTALLINE-SILICON MICROWAVE MEMS DEVICES Multi-Stable Switches, W-Band Phase Shifters, and MEMS Tuneable Frequency-Selective Surfaces

JOACHIM OBERHAMMER* *, MIKAEL STERNER, AND NUTAPONG SOMJIT

Royal Institute of Technology (KTH), School of Electrical Engineering, Microsystem Technology Laboratory

Abstract Monocrystalline silicon is still the material of first choice for robust MEMS devices, because of its excellent mechanical strength and elasticity, and the large variety of available standard processes. Conventional RF MEMS components consist of thin-film metal structures which are prone to plastic deformation and limit the power handling. The microwave MEMS devices presented in this work utilize monocrystalline silicon as the structural material of their moving parts, and even prove that highresistivity silicon is a good dielectric material in the W-band. A very low insertion loss, mechanically multi-stable, static zero-power consuming, laterally moving microswitch concept completely integrated in a 3D micromachined transmission line is presented. Furthermore, a multi-stage phase shifter utilizing high-resistivity monocrystalline silicon as dielectric material for the MEMS-actuated moving block loading the transmission line is shown. Finally, a tuneable high-impedance surface based on distributed MEMS capacitors with a transfer-bonded monocrystalline silicon core is presented. Prototypes of these devices were fabricated and characterization results of the microwave and their actuator performance are given.

Keywords: :RF MEMS, phase shifter, microswitch, high-impedance surface, monocrystalline silicon.

1. Introduction Micro-electromechanical systems (MEMS) are integrated microdevices combining electrical components with passive (sensing) and active (actuationn) interface functions to their physical surroundings. Typical examples for sensors include pressure sensors, microphones, accelerometers, gyros, gas sensors, and bolometers; and examples for actuator functions are inkjet print-head nozzles, gas valves, microswitches, and optical micromirror arrays for projection devices. The actuation and sensing functions might

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** Joachim Oberhammer, Tel.: +46 8 790 62 50 Fax: +46 8 100 858; E-mail: joachim.oberhammer @ee.kth.se

E. Gusev et al. (eds.), Advanced Materials and Technologies for Micro/Nano-Devices, Sensors and Actuators, DOI 10.1007/978-90-481-3807-4_7, © Springer Science + Business Media B.V. 2010

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be integrated on the same chip, as for a gas flow controller, or a reciprocal mechanism combining sensing and actuation in one and the same element might be employed, such as an ultrasonic transducer [1–3]. The market potential and impact on society of MEMS devices is enabled by their fabrication being based on standard, mature high-volume semiconductor manufacturing processes and materials offering high miniaturization, large product uniformity, and low cost in high volumes; and by the existing capacity of high volume production facilities and logistics. RF MEMS are MEMS devices which are interacting with electrical signals from DC up to sub-millimeter waves, by switching, modulating, matching, tuning, and filtering. Typical devices are micromachined switches [4, 5], mechanically tuneable capacitors [6], micromachined inductors [7], micromechanical resonators for filters and as frequency base [8], tuneable loaded lines for phase shifters [9] or impedance matching circuits [10], reconfigurable antennas [11], and 3D micromachined transmission lines [12]. In general, RF MEMS devices are characterized by near ideal signal handling performance in terms of insertion loss, isolation, linearity, large tuning range, and by keeping these performance parameter over a very large bandwidth [4, 13]. On the other hand, the commercialization of RF MEMS devices is delayed by reliability issues [14], packaging and integration requirements [13], limited power handling capability, and by the fact that established competing low-cost technologies often offer sufficient performance for large volume key applications especially in the lower price segment. Microwave MEMS are RF MEMS devices which operate with signal frequencies above 30 GHz. With applications moving to higher and higher frequencies, the performance advantages of MEMS devices over their competitors are getting larger. Also, at frequencies where the signal wavelengths are getting closer to the device dimensions, it is possible to miniaturize a complete RF system on a chip, and different ways of interaction between the microwave signals and the micromechanics lead to new classes of RF MEMS devices [15]. Even if, in recent years, silicon micromachining has been rapidly augmented with new material and processes [2], monocrystalline silicon, besides silicon carbide, still is the most robust and reliable structural material for micromachined devices. Its yield strength exceeds steel by a factor of 2–3, and it maintains its elastic properties under large stress levels even when exposed to elevated temperatures [16]. Monocrystalline silicon is available as high-purity low-cost substrate, can be supplied in a large variety of doping levels, and has good thermal conductivity. Because of these advantages, in combination with silicon offering the largest variety of wafer-scale micromachining processes, silicon is still the best suitable material for integrated microsystems with high demands on mechanical reliability [1]. Monocrystalline silicon has been successfully applied to a variety of MEMS devices including pressure sensors, accelerometers [17], undeformable sub-nm-flatness micromirror arrays [18], and robust microrelays [19, 20]. Conventional RF MEMS devices for microwave applications are based on movable thin metallic bridges, either employed as capacitive switches [21] or as tuneable capacitors for distributed MEMS transmission line phase shifters [9]. In contrast to silicon, such metallic bridges have the disadvantage of being susceptible to plastic deformation, especially at slightly elevated temperatures above 80 ◦ C where gold, the most favored material because of its low resistivity, quickly looses its elastic properties. Furthermore, these bridges must be thin enough for actuation at acceptable actuation voltages which drastically limits the power handling. Besides silicon being an excellent structural material for MEMS moving elements, high-resistivity silicon (HRS) is also a promising substrate material for RFIC tech-

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nology. HRS substrates, including silicon-on-insulator (SOI) wafers, are available at relatively low cost with a controllable bulk resistivity as high as 8 k Ω cm, which guarantees for sufficiently low losses even if not reaching the resistivity of good microwave GaAs or quartz substrates of 107 k Ω cm. However, for transmission lines fabricated on HRS substrates, free carriers within the interface between the silicon and the silicon dioxide layer on the surface reduce the effective resistivity by more than one order of magnitude, which necessitates the application of surface passivation techniques [22]. The present work describes microwave MEMS devices developed at the Royal Institute of Technology, Stockholm, Sweden, during 2005–2008. All devices are based on monocrystalline bulk silicon as the structural and in some cases also as the dielectric material. A very low insertion-loss, mechanically multi-stable, static zero-power consuming, laterally moving microswitch concept with its actuation mechanism integrated into a coplanar waveguide is presented in Section 2. Furthermore, in Section 3, a loaded-line phase shifter is discussed which utilizes high-resistivity monocrystalline silicon as dielectric material for a moving block, proving the good microwave properties of HRS by its excellent performance throughout the whole W-band. Finally, in Section 4, a tuneable high-impedance surface based on distributed MEMS capacitors with a transfer-bonded monocrystalline silicon core for high-reliability is presented.

2. Mechanically multi-stable, CPW embedded microswitches The presented electrostatically actuated metal-contact RF MEMS switch concept, illustrated in Figure 1, combines the following special features in a very unique way: – Mechanical multi-stability The switch designs are fully mechanically stable in both the on-state and in the off-state, i.e. the states are maintained without applying any external actuation energy, resulting in true static zero-power-consumption. External voltage only needs to be applied for the transition between the stable states. Conventional MEMS switches need external driving voltage at least in one of the states, and even if very low-power electrostatic actuation is employed, the driving circuitry of such switches consumes a considerable amount of energy. The mechanical bi-stability of the presented single-pole-single-through (SPST) twoport designs is achieved by perpendicularly arranged cantilevers with interlocking hooks. The actuation sequence for interlocking and for unlocking the cantilevers in

Figure 1. Conceptual illustration of the presented static zero-power-consumption coplanarwaveguide integrated metal-contact MEMS switch.

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Switch OFF

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the transition between the on and the off-state is shown in Figure 2. The singlepole-double-through (SPDT) three-port devices as shown in Figure 3d consist of cantilevers for each output port which can be interlocked with the cantilever(s) of the input port [24, 25]. Coplanar-waveguide signal-line integration: Since the current in a coplanar waveguide transmission line is confined to the edges of the metal conductors, the inside of the signal line is field-free. Thus, the complete switch mechanism is placed inside the signal line of a coplanar waveguide transmission line, which results in much lower impact on the wave propagation in the slots, as compared to conventional MEMS switches where the actuator is built on top of the transmission line. Two switch interlocking cantilever mechanisms are placed symmetrically on each side of the signal line to maintain a balanced wave propagation mode in the two signalto-ground gaps. The transmission line employed in this design is a 3D micromachined coplanar waveguide, where, in contrast to planar coplanar waveguides were the current is crowded in the thin edges of the metal lines, the currents are propagating in the metalized side-walls of the 30 µm deep trenches. This reduces dielectric substrate losses, since most of the electric field lines are concentrated in the open space and not penetrating into the substrate, and also decreases ohmic losses since the skin-depth limits the current mainly laterally [23]. Active opening capability: For the present concept, the transition from the off-state of the on-state is done by actively separating the contacts by electrostatic forces, in contrast to most MEMS switches which are passively opened by a very limited restoring spring force. The active opening capability ensures large opening forces potentially improving the contact reliability and allowing for soft metal contacts with low contact resistance and low material resistivity, such as gold [26]. Uncomplicated fabrication of the switches together with the 3D transmission lines by bulk micromachining deep reactive ion etching of the structures 30 µm deep into the device layer of a high-resistivity silicon (>4 k Ω cm) SOI wafer, followed by a wet release of the moving parts by underetching the burried-oxide (BOX) layer in hydrofluoric acid, by a mask-less gold sputtering deposition, and by an electrochemically-assisted selective gold etching process [27]. This fabrication procedure involves only a single photolithographical step and very few process steps, as compared to more complicated multi-mask surface-micromachined fabrication of conventional MEMS switch concepts. Mono-crystalline silicon is used as structural material for all moving parts, providing the best possible mechanical reliability, substantially better than deposited amorphous SiN or SiO2 or electroplated metal structures as used in conventional switch designs. Also, the symmetrical Au–Si–Au metallization of the cantilevers

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drastically eliminates susceptibility to changes in the operation temperature, a typical problem of multi-layer surface micromachined switches. – All-metal switch design: In conventional switches, dielectric layers are employed for preventing short-circuit between the actuation electrodes. Dielectric materials are prone to charging effects resulting in non-reproducible actuation voltages up to rendering the switches inoperable. The present design does not utilize any dielectric layers but uses stopper structures for preventing short-circuit, and all walls are covered with metals [26]. Figure 3 shows scanning electron microscopy (SEM) pictures of three two-port (SPST) and a three-port (SPDT) design, the latter embedded into the T-junction of 3D micromachined coplanar waveguides. Figure 3e, f show the SPST design variant A in its locked and unlocked state. In these close-up views, the 3D structrures of the laterally moving cantilevers and the deep-etched grooves in the transmission lines are visible. For the two-port devices, the two cantilevers of each interlocking-mechanism pair are designed for a deflection of 2.5 and 4.5 µm, and the DC actuation voltages were measured to 23 and 39 V, respectively. The total DC resistance of the closed switches including their 500 µm long transmission line pieces is between 0.9 and 1.2 Ω . The mechanical robustness of the laterally moving switch cantilevers has been verified up to 1.5 × 108 switch cycles at signal current of 1.5 µA and a switching frequency of 3 kHz, after which the tests were discontinued without observing any failure. The RF performance is summarized in Figure 4a, showing the isolation and reflected power of the three SPST design variants in their off state. Figure 4b–d compare the insertion loss and reflections of the three SPST design variants in their closed states to each other and also to straight transmission line pieces and signal lines shaping the geometry of the switch mechanism. The total insertion loss of the best design, variant C, including its transmission line was measured to less than

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–0.15 and –0.35 dB at 2 and 10 GHz, respectively. The isolation for the same design was determined to –45 and –25 dB at 2 and 10 GHz, respectively. The 3D micromachined transmission lines alone where found to have a loss of less than –0.4 dB/mm up to 10 GHz. When taking into account the losses of the straight transmission line pieces alone, the geometry and the switch mechanism of design variant C has an insertion loss of less than –0.08 dB up to 20 GHz, which demonstrates the low intrusive RF design. For the T-junction SPDT switches, the isolation in the open state was measured to –43 and –22 dB at 1 and 10 GHz, respectively. The total insertion loss of the closed switch including the T-junction was determined to –0.31 and –0.68 dB at 1 and 10 GHz, respectively, and the line reflections in the on-state are –29 and –22 dB at these frequencies. Reference measurements show that the insertion loss of a solid signal line in the T-junction amounts to the major part of the losses with –0.15 and –0.43 dB at 1 and 10 GHz, respectively.

3. W-band 4.25 bit MEMS moving dielectric-block phase shifter The concept of a single stage of the novel phase shifter concept is depicted in Figure 5. A monocrystalline high-resistivity silicon (>4 k Ω cm) dielectric block is placed on top

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Figure 5. Concept of the MEMS movable dielectric block phase shifter [28].

of a 1 µm thick gold coplanar waveguide. The relative phase shift ∆φ is achieved by vertically moving the dielectric block above the transmission line by electrostatic actuation, which results, due to the modulation of the capacitive load of the line, in varying propagation constants of the microwave signal in the transmission line. Silicon is a very suitable material for this task because of its high dielectric constant of 11.9, resulting in high sensitivity to the block position. The 50 µm deep etched slots into the high-resistivity silicon substrate decrease substrate loss and decrease the effective ǫr of the transmission line, thus further increasing the sensitivity to the silicon dielectric block. The length of the dielectric block is chosen to be λ/2 at the nominal frequency of 75 GHz to minimize the RF signal reflection from both edges of the dielectric block. For digital-type operation (up-state or pulled-in), an initial distance of the block of 5 µm to the transmission line is chosen, which is an optimum operation point compromising high phase-shift sensitivity with a displacement realizable by MEMS electrostatic actuators. The silicon blocks are fabricated by polymer transfer bonding [29] of a complete 30 µm thick silicon device layer from an SOI wafer to the target wafer, by subsequent removing of the SOI handle wafer and by structuring the block with its mechanical springs by different deep-reactive-ion etching steps. Dielectric charging of the block in the downstate is avoided by small SiN distance keepers [28].

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Figure 6. (a) SEM picture of a 45◦ , a 30 ◦, and a 15 ◦ stage in series; (b) 7-stage phase phase shifters at 75 GHz: binary coded 5 × 45◦ + 30◦+15◦ phase shifter (left), and 7 × 45◦ linear coded phase shifter (right).

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Figure 7. Performance of the binary coded phase shifter for the W-band: (a) insertion loss and return loss for actuating 1–7 stages; (b) phase shift per length and phase shift per loss. Nonlinearity investigation: (c) relative phase shift of a 45◦ stage depending on signal power; (d) intermodulation product and intercept point of third order.

For releasing the silicon block, the polymer sacrificial layer is etched through etchholes in the block. When properly choosing the etch-hole sizes, which are in the order of 100 times smaller than the wavelength, the effective dielectric constant of the block can be tailor-made, giving the possibility of designing phase-shifter stages of different relative phase shifts out of the same material. Figure 6a shows a SEM picture of three stages with different etch-hole sizes, resulting in a 45◦ , a 30◦ , and a 15◦ phase shift. Figure 6b presents multi-stage phase shifters constructed with these stages: a 4.25 bit binary coded phase shifter with 15◦ resolution and a maximum phase shift of 270◦ at 75 GHz, consisting of 5×45◦ +1×30◦ +1×15◦ stages, and a linear coded 3 bit phase sifter with a resolution of 45◦ and a maximum phase shift of 360◦ at 75 GHz, created by 7 × 45◦ stages. Figure 7a, b summarize the performance of the binary coded phase shifter: the maximum insertion loss and return loss at the design frequency of 75 GHz is –3.5 and –17 dB, respectively, and the maximum insertion and return loss in the whole 75–110 GHz band are better than –4 and –12 dB. The phase shift per loss is 71.05 and 98.3 ◦ / dB at 75 and 110 GHz, respectively, and the phase shift per length is 490 and 716 ◦ /cm at these frequencies. These results of the first prototypes show the best

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maximum loss per bit and return loss ever reported for the whole W-band, 1 clearly proving the potential of this novel phase shifter concept. As any (MEMS) phase shifter, the moving parts in the up-state are susceptible to self-modulating their deflection, since the voltage on the signal line also exerts an attracting force, if the signal line voltage is modulated with a frequency lower than the mechanical resonance frequency (60 kHz for the presented designs). This demodulation effect of the RF signal is caused since the electrostatic force is proportional to the square of the voltage. Figure 7c shows the measured change in phase shift for a 45 ◦ stage in the up-state, depending on the signal line power. The phase error at 35 dBm signal power is still below 2%, but reaches quickly 4% at 40 dBm. This behavior results in an intermodulation intercept point of third order of 48 dBm up to a signal power of 30 dBm, which emphasizes the excellent linearity behavior of the device (Figure 7d). All moving parts, including the blocks and the mechanical springs, are fabricated out of the same monocrystalline silicon block, and no other materials are employed. This guarantees best reliability, which was proved by life-cycle tests. All tested devices could be actuated to 1 billion cycles in a nonhermetic environment without any failure, and after which the tests were discontinued. Also, in contrast to conventional MEMS phase shifters where the power handling is limited by the critical current density in the thin metallic bridges, the power handling of this phase shifter concept is not limited by the moving parts, but just by the actual transmission lines and the substrate as a heat sink.

4. MEMS tuneable high-impedance surfaces High-impedance surfaces (HIS) exhibit unnaturally high surface impedance approaching ±j∞ at their resonance frequency and have attracted attention because of their promising applications in improvement of antenna radiation patterns, suppression of surface waves [32] and phase shifting [33].

(a)

(b)

Figure u r 8. Illustration of (a) MEMS tuneable high-impedance surface; (b) reflective beam-steering with MEMS HIS [15].

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1 Except for [30] which has better performance at its nominal frequency only, but performs worse for the rest of the W-band, and is fabricated on glass substrate.

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(a)

(b)

Figure 9. (a) Cross-section of a single element [15]; (b) RF characterization [15, 31].

The concept of using distributed MEMS actuators for local tuning of the surface resonance frequency is illustrated in Figure 8a, along with the application in reflective millimeter-wave beam steering by a single chip, utilizing the phase-shifting effect of the surface since the reflection coefficient has a steep phase transition between +180◦ and –180 ◦ around its resonance frequency [34]. The micromachined elements uniquely unify electromechanical tuneability with microwave functionality in one and the same distributed high-impedance surface elements, thus presenting a new class of microsystems interacting with microwaves. The high-impedance surfaces presented in this section are composed of an array of electrostatically tuneable elements, based on vertically moveable conductive membranes and conductive patches on the surface of a ground-backed 100 µm thick low-loss glass substrate (Figure 9a). The process design of the membranes is quite unique in contrast to conventional MEMS tuneable capacitors which are based on thin metallic bridges: A 1 µm thick monocrystalline silicon core is used for the membrane to provide mechanical robustness and for optimized membrane flatness, and is transfer-bonded to the target substrate by adhesive bonding [29]. For electrical purpose, the membrane is clad on both sides by 0.5 µm gold, the top layer before and the bottom layer after the transfer bonding.

Figure 10. SEM pictures of a fabricated high-impedance surface array with close-up views [15].

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This symmetric deposition is designed for high process robustness, since it guarantees a stress-free sandwich structure without having to tune the stress in the metallic layers. The membrane is electrically and mechanically connected by meander shaped springs to the supporting metal posts, before free-etching of the membranes by plasma-etching the polymer bonding layer is done. Figure 10 shows SEM pictures of a fabricated prototype device, an array of a size of 70 × 18.5 mm 2 with 200 × 52 elements. The reflective properties of the surfaces were evaluated by back-short termination of a rectangular WR-10 waveguide, showing the characteristic phase transition of over 245◦ at 112 GHz, shown in Figure 9b [15, 31]. The actuation voltage was measured to 15.9 V, well corresponding to the 15.4 V predicted by FEM simulations.

Acknowledgements Funding for some parts of the work is provided through the NORDITE Scandinavian ICT Programme (VINNOVA, TEKES, RCN) and the European Community’s Seventh Framework Programme FP7/2007–2013 under grant agreement no. 224197.

References 1. G. T. A. Kovacs, Micromachined Transducers Sourcebook, 1st ed. New York: McGrawHill, 1998. 2. C. Liu, Foundations of MEMS. Pearson Prentice Hall, 2006. 3. M. J. Madou, Fundamentals of Microfabrication: the science of miniaturization, 2nd ed. Boca Raton, London, New York, Washington D.C.: CRC Press, 2002. 4. G. M. Rebeiz, RF MEMS Theory, Design and Technology, 1st ed. Hoboken, New Jersey: Wiley, 2003. 5. E. Brown, “RF-MEMS switches for reconfigurable integrated circuits,” IEEE Transactions on Microwave Theory and Techniques, vol. 46, no. 11, pp. 1868–1880, 1998. 6. H. D. Nguyen, D. Hah, P. R. Patterson, R. Chao, W. Piyawattanametha, E. K. Lau, and M. C. Wu, “Angular vertical comb-driven tunable capacitor with high-tuning capabilities,” IEEE Journal of Microelectromechanical Systems, vol. 13, no. 3, pp. 406–413, June 2004. 7. H. Jiang, Y. Wang, J.-L. Yeh, and N. Tien, “On-chip spiral inductors suspended over deep copper-lined cavities,” IEEE Trans. on Microwave Theory and Techniques, vol. 48, no. 12, pp. 2415–2423, Dec. 2000. 8. C. T.-C. Nguyen, “MEMS technology for timing and frequency control,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 54, no. 2, pp. 251–270, Feb 2007. 9. G. M. Rebeiz, G.-L. Tan, and J. S. Hayden, “RF MEMS phase shifters: design and applications,” IEEE Microwave Magazine, vol. 3, no. 2, pp. 72–81, June 2002. 10. J. Papapolymerou, K. Lange, C. Goldsmith, A. Malczewski, and J. Kleber, “Reconfigurable double-stub tuners using MEMS switches for intelligent RF front-ends,” IEEE Trans. on Microwave Theory and Techniques, vol. 51, no. 1, pp. 271–278, Jan. 2003. 11. B. Cetiner, J. Qian, H. Chang, M. Bachman, G. Li, and F. De Flaviis, “Monolithic integration of RF MEMS switches with a diversity antenna on PCB substrate,” IEEE Trans. on Microwave Theory and Techniques, vol. 51, no. 1, pp. 332–335, Jan. 2003. 12. I. Llamas-Garro and A. Corona-Chavez, “Micromachined transmission lines for millimeterwave applications,” in Electronics, Communications and Computers, 2006. CONIELECOMP 2006. 16th International Conference on, 2006, pp. 15–15. 13. H. A. C. Tilmans, W. De Raedt, and E. Beyne, “MEMS for wireless communications: ‘‘from RF-MEMS components to RF-MEMS-SiP’,” IOP Journal of Micromechanics and Microengineering, vol. 13, no. 4, pp. S139–S163, July 2003. 14. J. DeNatale and R. Mihailovich, “RF MEMS reliability,” in Proc. Transducers 2003, Boston, MA, USA, June 8–12, 2003, pp. 943–946.

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15. M. Sterner, D. Chicherin, A. V. R¨ ais¨ anen, G. Stemme, and J. Oberhammer, “RF MEMS high-impedance tuneable metamaterials for millimeter-wave beam steering,” in Proceedings IEEE/ASME Micro-Electro-Mechanical Sytems MEMS 2009, Sorrento, Italy, Jan. 25–29, 2009, pp. 896–899. 16. K. Petersen, “Silicon as a mechanical material,” Proceedings of the IEEE, vol. 70, no. 5, pp. 420–457, May 1982. 17. T. Fujita, Y. Fukumoto, F. Suzuki, and K. Maenaka, “SOI-MEMS sensor for multienvironmental sensing-system,” in Proc. IEEE Networked Sensing Systems, 2007, Braunschweig, Germany, June 6–8, 2007, pp. 146–149. 18. F. Niklaus, S. Haasl, and G. Stemme, “Arrays of monocrystalline silicon micromirrors fabricated using CMOS compatible transfer bonding,” IEEE Journal of Microelectromechanical Systems, vol. 12, no. 4, pp. 465–469, Aug. 2003. 19. M. Sakata, Y. Komura, T. Seki, K. Kobayashi, K. Sano, and S. Horiike, “Micromachined relay which utilizes single crystal silicon electrostatic actuator,” in Proc. IEEE Micro Electro Mechanical Systems 1999, Orland, FL, USA, Jan. 17–21, 1999, pp. 21–24. 20. A. Weber, J. Lang, and A. Slocum, “{111} Si etched planar electrical contacts for power MEMS-relays,” in 53rd IEEE Holm Conference on Electrical contacts – 2007, Pittsburgh, PA, USA, Sept. 16–19, 2007, pp. 156–159. 21. C. Goldsmith, J. Ehmke, A. Malczewski, B. Pillans, S. Eschelmann, Z. Yao, J. Brank, and M. Eberly, “Lifetime characterization of capacitive RF MEMS switches,” in Proc. IEEE MTT-S Int. Microwave Symposium, Phoenix, AZ, USA, May 20–25, 2001, pp. 779–808. 22. D. Lederer and J.-P. Raskin, “New substrate passivation method dedicated to HR SOI wafer fabrication with increased substrate resistivity,” IEEE Electron Device Letters, vol. 26, no. 11, pp. 805–807, Nov. 2005. 23. M. Sterner, N. Roxhed, G. Stemme, and J. Oberhammer, “Coplanar-waveguide embedded mechanically-bistable DC-to-RF MEMS switches,” in IEEE/MTT-S International Microwave Symposium (IMS), Honolulu, HI, USA, June 3–8, 2007, pp. 359–362. 24. J. Oberhammer, M. Tang, A.-Q. Liu, and G. Stemme, “Mechanically tri-stable, true singlepole-double-throw (SPDT) switches,” Journal of Micromechanics and Microengineering, vol. 16, no. 11, pp. 2251–2258, September 2006. 25. M. Sterner, N. Roxhed, G. Stemme, and J. Oberhammer, “Mechanically tri-stable SPDT metal-contact MEMS switch embedded in 3D transmission line,” in 37th European Microwave Conference (EuMC), Munich, Germany, Oct. 8–12, 2007, pp. 1225–1228. 26. J. Oberhammer and G. Stemme, “Active opening force and passive contact force electrostatic switches for soft metal contact materials,” Journal of Microelectromechanical Systems, vol. 15, no. 5, pp. 1235–1242, 2006. 27. M. Sterner, N. Roxhed, G. Stemme, and J. Oberhammer, “Maskless selective electrochemically assisted wet etching of metal layers for 3d micromachined soi rf mems devices,” in IEEE 21st International Conference on Micro Electro Mechanical Systems (MEMS), Jan. 2008, pp. 383–386. 28. N. Somjit, G. Stemme, and J. Oberhammer, “Novel concept of microwave MEMS reconfigurable 7 ×45◦ multi-stage dielectric-block phase shifters,” in Proc. IEEE/ASME Micro Electro Mechanical Systems 2009, Sorrento, Italy, Jan. 25–29, 2009, pp. 15–18. 29. F. Niklaus, P. Enoksson, P. Griss, E. K¨ alvesten, and G. Stemme, “Low-temperature waferlevel transfer bonding,” IEEE Journal of Microelectromechanical Systems, vol. 10, no. 4, pp. 525–531, 2001. 30. J. Hung, G. Dussopt, and M. Rebeiz, “Distributed 2- and 3-bit W-band MEMS phase shifters on glass sustrates,” IEEE Transactions on Microwave Theory and Techniques, vol. 52, no. 2, pp. 600–606, Feb. 2004. 31. D. Chicherin, S. Dudorov, J. Oberhammer, M. Sterner, and A. V. R¨ ais¨ anen, “Microfabricated high-impedance surface for millimeter wave beam steering applications,” in Proc. of 33rd International Conference on Infrared, Millimeter, and Terahertz Waves, Pasadena, CA, USA, Sept. 15–29, 2008. 32. D. Sievenpiper, “High-impedance electromagnetic surfaces,” Ph.D. dissertation, Dept. Elect. Eng., Univ. of California, Los Angeles, 1999. 33. J. Higgins, H. Xin, A. Sailer, and M. Rosker, “Ka-band waveguide phase shifter using tunable electromagnetic crystal sidewalls,” IEEE Trans. Microw. Theory and Techniques, vol. 51, no. 4, pp. 1281–1288, April 2003. 34. D. Chicherin, S. Dudorov, D. Lioubtchenko, V. Ovchinnikov, and A. R¨ ais¨ anen, “Millimetre wave phase shifters based on a metal waveguide with a MEMS-based high-impedance surface,” in Proceedings of the 36th European Microwave Conference, September 2006, pp. 372–375.

THREE-DIMENSIONAL PHOTONIC CRYSTALS BASED ON OPAL-SEMICONDUCTOR AND OPAL-METAL NANOCOMPOSITES

VALERY G. GOLUBEV Ioffe Physical-Technical Institute RAS, 26 Polytekhnicheskaya street, St Petersburg 194021, Russian Federation, E-mail: [email protected]

Abstract This paper presents an overview of our recent activity on fabrication and investigation of three-dimensional opal-semiconductor and opal-metal photonic crystals. The main goal of our work is to create materials where functional properties of opal pore fillers could be combined with unique features of photonic crystals based on synthetic opals. The novel properties of such materials open new possibilities to mould and control emission and propagation of light in visible and near-infrared photonic and optoelectronic devices.

Keywords: Photonic crystal, synthetic opal, photonic band gap, semiconductor, metal, emitting properties, optical switching, phononic band gap.

1. Introduction Photonic crystals (PCs) – materials with a periodical modulation of dielectric permeability on the scale of the order of the light wavelength – are most promising candidates for making photonic microchips. The photonic band structure of such materials is determined by the PCs lattice period and symmetry and also by the dielectric contrast, i.e., the ratio between dielectric permeabilities of the components that comprise the PCs. Similar to the forbidden band gap structure of atomic crystals, the PCs have frequency regions (photonic band gaps – PBGs) in which light propagation inside the PC is suppressed in one direction or all crystallographic directions (a complete PBG). PBG results from Bragg diffraction of electromagnetic waves from the periodic PC structure [1–4]. It is just the PBG that allows control of spontaneous emission and leads to light localization. This opens up the way to application of PCs in optical communication and information transmission systems, laser technology, quantum computers, etc. A good example of a 3D PC, i.e., a crystal possessing a PBG, is synthetic opal. Synthetic opals have a face-centered cubic (fcc) lattice made up of closely packed monodisperse amorphous SiO2 (a-SiO2) spheres with a diameter varying in E. Gusev et al. (eds.), Advanced Materials and Technologies for Micro/Nano-Devices, Sensors and Actuators, DOI 10.1007/978-90-481-3807-4_8, © Springer Science + Business Media B.V. 2010

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the range of 100–1,000 nm. The PBG position and width can be changed from the ultra-violet to near-infrared regions by varying the a-SiO2 sphere size and by filling the interconnected opal pores with various functional materials having a refractive index different from that of a-SiO2 [4]. This report presents experimental results on spontaneous emission and its control with a specially synthesized three-dimensional (3D) PCs based opal-Er [5] and opal-phosphor [6, 7] nanocomposites. The report describes also experimental demonstration of a femtosecond control of light beams in high-contrast opal-Si [8, 9] and opal-VO2 [10, 11] PCs where the complete PBG can be implemented. An ultrafast control of light beams is achieved by changing the dielectric permeability of a semiconductor at photoexcitation when free carriers are generated in it. As a result, the optical properties of the nanocomposites can be governed by an external light source, which is promising for all-optical switching applications. The periodicity of dielectric constants in opals is accompanied by a periodicity of acoustic impedance. The elastic coupling between a-SiO2 spheres composing opal films brings forth 3D periodic structures which, in addition to the PBG, are predicted to exhibit complete phononic band gaps. In this report, the influence of elastic crystal vibrations on the photonic band structure studied by injection of coherent hypersonic wave packets generated in a metal transducer by subpicosecond laser pulses is demonstrated. These studies show that light with the energies close to the PBG is efficiently modulated by hypersonic waves [12].

2. Luminescence properties of opal–erbium nanocomposites In the present study, the trivalent erbium ion Er3+ was chosen as an emitting center to be embedded in an opal matrix. Erbium-containing materials enjoy broad application in telecommunications and optoelectronics [13]. The wavelength of the main Er3+ ground-state transition, 1.54 µm, coincides with the standard wavelength in use in optical telecommunication systems determined by the quartz waveguide transparency window. The Er3+ ion can also efficiently emit light at other discrete wavelengths in the visible and near-IR spectral regions determined by the structure of the excited states of this ion [13]. It is essential that the optical transitions occur in the 4f 11 inner shell of the Er3+ ion, which is screened by the outer electronic shells; therefore, the spectral widths of the corresponding emission lines are narrower than the opal PBG width. We chose synthetic opals with a polydomain structure as the starting matrices. The size of a domain with a highly ordered a-SiO2 sphere arrangement was 30–100 µm. Samples were platelets 5 × 5 × 0.1 mm in size cut parallel to the opal (111) plane. The SiO2 sphere diameter was 230 ± 5 nm. The dimensions of interconnected octahedral and tetrahedral pores were roughly 90 and 45 nm, respectively. The opal pores were initially filled with erbium nitrate in the form of a water solution at room temperature. Subsequent thermal decomposition of the erbium nitrate (at 500°C over 1 h) produced erbium oxide Er2O3 in the pores. The volume

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fraction of filled opal pores was determined gravimetrically to be approximately 11% of the total pore volume. Because of the use of a water solution, the Er2O3 formed in pores contained a large amount of hydroxyl groups, which are strong quenchers of Er photoluminescence (PL) [13]. To reduce the concentration of hydroxyl groups and increase the PL intensity, the samples were annealed in air at 850°C for 1 h. To study the emitting properties of the opal–Er composite, PL spectra were measured at nitrogen temperature in the visible and near-IR ranges. The Er3+ photoluminescence was excited with an Ar+ laser at a wavelength of 488 nm (in the vicinity of the 4I15/2 → 4F7/2 transition in the 4f11 shell of the Er3+ ion). The laser beam was focused on the sample to a spot 0.5 mm in diameter. The incident power density did not exceed 5 W/cm2.

Figure 1. Photoluminescence spectrum of the opal–Er composite obtained at nitrogen temperature in the (a) visible and (b) near-IR region. The sample was annealed in air at T = 850°C for 1 h. Peaks 1–5 are Er3+ photoluminescence lines corresponding to the transitions 4 S3/2 → 4I15/2 (550 nm), 4S3/2 → 4I13/2 (860 nm), 4I11/2 → 4I15/2 (980 nm), 4S3/2 → 4I11/2 (1240 nm), and 4I13/2 → 4I15/2 (1540 nm) respectively.

It has been shown that Er is contained in two phases, one of which is amorphous, in the form of a layer on the surface of a-SiO2 spheres, and the other is polycrystalline, in filled pores whose fraction is small. Electron microscope studies revealed that Er is deposited on the pore surface as a thin amorphous coating (presumably, Er2Si2O7) in practically all pores. This permits one to maintain that it is this phase that Er predominantly enters. Only a small fraction of pores is filled completely with polycrystalline Er2O3. Optical measurements showed that the synthesized opal–Er composite retains the PBG properties of the original opal matrix.

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When pumped resonantly at a wavelength of 488 nm (4I15/2 → 4F7/2 transition), erbium in the composite efficiently emits light in the visible and near IR regions at several discrete wavelengths corresponding to the radiative transitions (Figure 1). Thus, opal–Er nanocomposites combine the PBG properties of opal with the luminescence of Er and can serve as a model object to study the effect of the PBG on the spontaneous emission of radiating centers [5].

3. Electroluminescent three-dimensional photonic crystals based on opal-phosphor nanocomposites In this section, electroluminescent PCs produced by synthesizing the phosphors Zn2SiO4:Mn and ZnS:Mn in opal pores are presented. High luminosity of the emission of these phosphors is due to the intracenter electron transition 4T1 → 6A1 in the 3d-shell of a Mn2+ ion. The transition energy depends on the symmetry of the crystal field, in which this ion is localized. For example, the electroluminescence (EL) peak of Zn2SiO4:Mn is in the green region while that of ZnS:Mn is in the orange region. Details of fabrication of opal-phosphor nanocomposites can be found elsewhere [6, 7]. EL structures were made from synthesized composites by depositing a conductive semitransparent indium-tin oxide layer on one PC facet and a layer of BaTiO3 powder dispersed in an organic compound on another, followed by deposition of a silver paste layer [6]. The structures were excited by an AC electric field, whose characteristics were well below the breakdown threshold (strength ~104–105 V/cm, frequency 0.1–2 kHz). To study the PBG properties of the composites, we measured the angular resolved spectra of Bragg reflection from the (111) surface. The study of the PBG effect on the EL spectra requires that the PBG positions of the composites be overlapped by their emission spectra. The modification of the EL spectrum due to the change of the registration angle is presented in Figure 2a with reference to opal-GaN-ZnS:Mn. One can see that there is a dip in the emission spectrum in the region where the (111) reflection peak (Figure 2b) overlaps with its EL spectrum. When the detection angle increases relative to the normal to the surface, the dip in the EL spectrum is shifted to shorter wavelengths following the shift of the reflection maximum, which obeys Snell’s formula [14]. The sulfide (ZnxCd1−xS:Mn and ZnxCd1−xS:Ag) phosphors were also synthesized directly inside the pores of synthetic opal by chemical bath deposition and their emission spectra are considerably modified by the PC structure to become anisotropic in accordance with the PBG angular dispersion [7]. To summarize, chemical bath deposition was used to produce 3D electroluminescent PCs based on opal-phosphors composites. We have demonstrated the possibility to excite visible light by applying an AC electric field to these PCs and to control the shape of emission spectra by varying the PBG position.

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Figure 2. The composite opal-GaN-ZnS:Mn: (a) the EL spectra registered at various angles relative to the normal to the (111) surface of the composite: 1 – 10°, 2 – 20°, 3 – 30°, 4 – 40°, 5 – 50°; (b) the spectra of reflection from the (111) composite surface at various light incidence: 1 – 10°, 2 – 20°, 3 – 30°, 4 – 40°, 5 – 50°.

4. Femtosecond all-optical switching in opal-Si photonic crystals One of the most interesting potential applications of PCs is all-optical switching. A light pulse from an external light source can change the complex dielectric constant and correspondingly change the PBG position and its width, thus, realizing all-optical switching. In this chapter, the results on the transient change in reflectivity of a-nc-Sibased 3D PCs induced by strong irradiation of a femtosecond light pulse are demonstrated. A sketch of our structure is shown in the inset to Figure 3. As a filling substance amorphous-nanocrystalline Si (a-nc-Si) is further advantageous because of its high index of refraction and its suitability to be integrated into microelectronic technology. The voids of the opal were filled with mixed a-nc-Si

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up to a filling factor close to 100% by thermal decomposition of a 5%-SiH4–Ar gas mixture. The sample was cut in a 0.5-mm thick plate almost parallel to the (111) surface. Further details of the sample fabrication can be found in Ref. [15].

Figure 3. Measured (□) and calculated (––) spectra of Bragg diffraction efficiency of an a-nc-Sibased PC. Insert shows a sketch of the fcc opal-Si structure.

The stationary Bragg reflectance spectra were measured with a halogen lamp and detected by a spectrometer equipped with a CCD. All time-resolved reflectivity measurements were performed by a conventional pump-probe technique [8, 9]. The temporal evolution of the relative transient change in the Bragg reflection ∆R(t)/R induced by a strong (5 mJ/cm2) optical pump pulse is shown for three probe wavelengths in Figure 4, the solid curve at 780 nm (PBG region), and the dashed at 760 nm and dotted curves at 850 nm (wings of the PBG). The reflection signal shows an abrupt decrease directly after the arrival of the pump pulse (t = 0) and partly recovers on a picosecond timescale. The changes in the Bragg reflection are maximum at the PBG where they reach ∆R(t)/R = –46%. The inset to Figure 4 displays the time trace of ∆R(t)/R measured at λ = 800 nm at a lower pump power density (70 µJ/cm2) and higher temporal resolution. Here, the amplitude of the relative changes in reflectivity is ∆R/R = −1.2 × 10−2. The initial peak in ∆R/R occurs when pump and probe overlap in time and can be explained by the instantaneous Kerr effect. The decay at longer delays appears to have a multi-exponential shape with the time constants τ ~ 0.5 ps and τ ~ 5 ps. The fact that the ultrafast switching takes place within 30 fs suggests that induced changes are caused by photoexcited carriers in a-nc-Si. Photoinduced changes in the real and imaginary parts of the a-nc-Si refractive index suppress the Bragg interference of the light inside the PC and diminish the Bragg reflection. This results in a rapid switching of the reflectivity of the opal-a-nc-Si nanocomposites on the detected wavelength.

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Figure 4. Time-resolved transient differential reflection ∆R(t)/R at 760 nm (- - -), 780 nm (––), and 850 nm (······) in case of high-power (5 mJ/cm2) optical pulse excitation. Insert shows ∆R(t)/R at 800 nm in case of moderate (70 µJ/cm2) optical pulse excitation, measured with a higher temporal resolution (30 fs).

In conclusion, we have demonstrated a strong ultra-fast response in the reflectivity of a-nc-Si-based 3D PCs. It is shown that the switching time is less than 30 fs and determined by the pump pulse duration. The recovery time is in the order of several picoseconds. The observed transient changes in the Bragg reflectivity at high excitation power density can be as high as 46%. Our results are relevant for realizing an all-optical switching device based on a-nc-Si and operated at the sub-picosecond timescale.

5. Subpicosecond switching of the photonic band gap in opal-VO2 photonic crystal governed by a photoinduced semiconductor– metal phase transition One way to switch the spectral position of a PBG is to use a photoinduced phase transition, accompanied by permittivity changes of the constituents forming the 3D PC. The excitation of the PC material by intense laser pulses with a photon energy higher than its fundamental band gap generates hot carriers which, in turn, induces the phase transition directly or indirectly via generation of phonons. In both cases the temporal and spatial evolutions of the photoinduced phase transition during and after the laser pulse are governed by the kinetic properties of the photoexcited quasiparticles (electrons, phonons, plasmons, etc.). In this chapter, we present femtosecond shifting of the PBG in a synthetic opal filled with vanadium dioxide (VO2). The samples were fabricated from an opal template composed of 240 µm diameter monodispersed (±5%) a-SiO2 spheres. The voids of the opal were impregnated with VO2. The details of the fabrication

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method and the linear optical properties can be found elsewhere [12]. We take advantage of the structural phase transition in VO2 at Tc = 67°C that can take place on the subpicosecond time scale [16]. In the spectral region of red light, the transition is accompanied by changes in the real part of the refractive index from n(VO2) ≈ 2.9 in the “cold” semiconductor phase to n(VO2) ≈ 2.3 in the “hot” metallic phase. The reflectivity spectrum from the (111) facet of the opal-VO2 composite shows a peak with a maximum at the energy position of the PBG. The inset in Figure 5 shows two spectra measured under steady-state conditions at T = 30 and 90°C, corresponding to the semiconductor and metal phases of VO2, respectively. The high-energy shift of the spectrum and therefore of the PBG at elevated T is due to changes in the average permittivity of the composite, induced by the phase transition. As the reflectivity spectra are not symmetric, for a quantitative description of energy shifts, the first moments of the measured spectra were analyzed and associated with the PBG spectral position. Figure 5 shows the hysteresis loop of the measured shift ∆E(T) relative to the energy in the semiconductor phase. We observe a shift up to 90 meV, which is the maximum possible value for the used technology of pore filling with VO2. The hysteresis behavior of ∆E(T) in the heating and/or cooling cycle is governed by the properties of the phase transition

Figure 5. Hysteresis loop for the temperature dependence of the Bragg reflectivity peak energy in the opal-VO2 composite measured in steady-state experiments. Inset: Reflectivity spectra in the semiconductor (T = 30°C) and metallic (T = 90°C) phases.

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in the opal-VO2 composite, the details of which can be found elsewhere [14]. The observation of a hysteresis behavior is a strong evidence of the high quality of the VO2 in the opal pores, as confirmed also by x-ray and Raman studies. Time-resolved pump-probe experiments were carried out using a pulsed Ti:sapphire laser with a regenerative amplifier (wavelength, 800 nm; pulse duration, 200 fs; and maximum pulse energy 10 µJ). For the probe, a sapphire plate was used to convert it into a broad band “white light” pulse. The pulse repetition rate was less than 10 kHz to provide thermal recovery of the sample between pulses. The pump beam density on the sample surface was W = 10–25 mJ/cm2. The spot sizes of the focused pump and probe beams on the sample surface were 100 and 20 µm, respectively. A variable optical delay line was used to adjust the separation t between pump and probe, providing a temporal resolution more than 100 fs [10, 11]. The spectral position of the reflectivity maximum shifts rapidly to higher energies within a time less than a picosecond and then continues to move further on a longer time scale. The inset in Figure 6 shows the temporal evolution of the spectral shift ∆E(t) = E(t) − E0 (E0 is the first moment of the reflectivity in the semiconductor phase) in 125 fs steps. The initial shift of ∆Ei = 25 meV occurs almost instantaneously with the laser pump pulse. The shift shown in the main panel of

Figure 6. Temporal evolution of the Bragg peak energy in the reflectivity spectrum for a pump excitation with W = 20 mJ/cm2. The horizontal arrows show the values of the ultrafast shift (∆Ei) and quasistationary shift (∆Et). The inset does the same with a high temporal resolution in the early time range.

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Figure 6 has been measured using a longer time step. After the subpicosecond spectral shift of ∆E(t), the shift to higher energies goes on and then tends to saturate at a level ∆Et = 60 meV after a few hundreds of picosecond. Our analysis of the experimental results is based on the fact that the photoinduced phase transition of the VO2 in the opal pores starts in a boundary layer with thickness dc of the optically excited PC surface. The value of dc is on the order of the penetration depth la of the pump light into the opal-VO2 composite. The ultrafast PBG shift due to the photoinduced phase transition in VO2 is determined by two quantities: dc and the fraction α of VO2 in each pore in the excited boundary layer which has undergone the phase transition. For instance, if all VO2 material in this layer become metallic, then α = 1. Otherwise α < 1, which means that not all VO2 crystallites are metallic within the thickness dc. The PBG shift would be equal to the one observed under continuous excitation only if α = 1 and dc were large enough to form a PBG such as in a uniform PC. The kinetics of the PBG shift is governed by the time evolution of dc and of α [11]. In conclusion, we have shown that the ultrafast kinetics of the PBG shift governed by a photoinduced phase transition in a 3D PC has two components. The first one is a subpicosecond shift which takes place almost instantaneously with the femtosecond laser pulse. The second component has a transient time about 100 ps and is governed by spatial redistribution of the semiconductor and metal phases inside the material volume which undergoes phase transition.

6. Hypersonic modulation of light by three-dimensional photonic and phononic band-gap material The periodicity of the dielectric constants in artificially grown structures is generally accompanied by a periodicity of the acoustic impedance. With regard to their acoustic properties they may therefore behave as phononic crystals, in analogy to PCs for light. If the structure acts as a PC operating in the visible, then it shows the features typical of phononic crystals for hypersonic (~1010 Hz) acoustic waves. The combination of optical and hypersonic properties in a single highly ordered periodic structure leads therefore to a new object comprising a photonic and phononic crystal. The opal films with 1 cm2 area were grown by a vertical deposition method [17] on a silica substrate. The a-SiO2 spheres formed a fcc opaline matrix with the (111) plane parallel to the substrate surface. Two samples (1 and 2) were investigated. The sphere diameter in the colloidal suspension was D = 360 nm for both samples. From the scanning electron microscopy it is shown that neighboring spheres are penetrating each other, which is a result of the sintering during the opal formation process. Thus there is a considerable elastic coupling, which may result in formation of a phononic band structure. The elastic coupling parameter χ in the formed photonic–phononic crystal can be defined as χ = D/2a − 1, where 2a is the distance between the centers of neighboring spheres [18].

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The idea of the experiment is to inject into the sample a picosecond coherent elastic wave packet from a hypersonic transducer and to make time-resolved measurements of the corresponding changes of the optical Bragg reflectivity spectrum. An aluminum film with a thickness of 100 nm was deposited on an opal sample surface. This metal film played the role of the hypersonic transducer for generation of a picosecond strain pulse to be injected into the opal film. For excitation, 0.3 ps pulses from a Ti:sapphire laser with a regenerative amplifier (λ = 800 nm, repetition rate 250 kHz, and maximum energy per pulse 1 µJ) were used. The pump beam was sent along a variable delay line and focused (200 µm spot diameter) on the metal transducer. The probe pulse was split from the same laser beam and was focused onto the silica substrate exactly opposite to the pump spot [12]. Figure 7a shows the measured reflectivity changes ∆R(t)/R0 for the two samples. R0 is the reflectivity of the probe beam in the absence of pump excitation at a wavelength of 800 nm on a flank of the Bragg peak. After a sharp rise at t = 0, pronounced oscillations of ∆R(t)/R0 are observed. When the background is subtracted, in both cases the oscillatory part of the measured signal cannot be described by a single period and depends on the sample.

Figure 7. (a) Measured ∆R(t)/R0 signals for the two samples. (b) Fourier transforms of the signals in (a). Open circles and dots correspond to samples 1 and 2, respectively.

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The origin of the oscillations in ∆R(t)/R0 is the elasto-optical effect. Coherent elastic vibrations modulate the period of the opal structure, which consequently results in modulation of the spectral position and width of the PBG. When the probe light wavelength corresponds to one of the spectral wings of the Bragg reflection spectrum the efficiency of the hypersonic light modulation increases enormously. This gives an essential advantage to the use of photonic–phononic crystals for light modulation over traditional acousto-optical materials. The experimentally observed peak at ~11 GHz (Figure 7b) has a frequency close to the purely radial Lamb mode (l = 1, n = 0) of the isolated a-SiO2 sphere at ν1,0 = 10.8 GHz. No distinct peak in the measured spectrum at ν2,0 = 9 GHz which corresponds to the fundamental quadruple mode (l = 2, n = 0) is observed. This frequency would represent the lower limit, if the spheres were decoupled. The exciting experimental fact is that the measured ∆R(t)/R0 spectrum (Figure 7b) clearly shows vibrations with frequencies well below the lowest quadruple mode ν2,0. Elastic vibrations with frequencies below the Lamb modes can exist only if the vibrational modes spread over a distance exceeding the extension of an isolated sphere. Thus the experimental results clearly evidence that the spheres are considerably coupled with each other and the vibrational modes demonstrate phononic crystal behavior. In summary, in 3D opal based photonic–phononic crystals light with a wavelength close to the PBG can be strongly modulated by hypersonic vibrations with frequencies of about 10 GHz [12]. The measured vibrational spectra consist of frequencies lower than the Lamb modes of isolated a-SiO2 spheres. This underlines the importance of elastic coupling between the elementary blocks forming the 3D photonic–phononic crystal. With such a joint system ultrafast manipulation and control of light beams by hypersonic waves in structures which have complete 3D photonic and phononic band gaps may become feasible, promising a new generation of acousto-optical devices.

7. Conclusion This paper reviewed the results on 3D opal-based photonic crystals preparation and optical studies. In order to provide functionality to photonic crystals fabricated, the synthetic opal samples were embedded with Er, phosphors, Si, and VO2. We showed some examples where opal-based photonic crystals were used to modify and control light propagation, since this could have considerable impact on novel photonic and optoelectronic devices. We have also demonstrated that opals possess properties of 3D photonic–phononic crystals. It opens the way for application of opals to micro-nano acousto-optic devices. Acknowledgments The work was supported by the Russian Academy of Sciences and the RFBR (project 08-02-00450a).

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References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

12. 13. 14 15.

16. 17. 18.

Photonic crystals. Advances in design, fabrication, and characterization. Ed. By K. Busch, S. Lölkes, R.B. Wehrspohn, and H. Föll. Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim, 2004. J.-M. Lourtioz, H. Benisty, V. Berger, J.-M. Gerald, D. Maystre, and A. Tchelnokov. Photonic crystals. Towards nanoscale photonic devices. Springer-Verlag Berlin Heidelberg, 2005. J.D. Joannopolous, S.G. Johnson, J.N. Winn, R.D. Meade. Photonic crystals. Molding the flow of light. Second edition. Prinston University Press. Prinston and Oxford, 2008. C. López. Materials aspects of photonic crystals. Adv. Mater. 15, 1679–1704 (2003). G.N. Aliev, V.G. Golubev, A.A. Dukin, D.A. Kurdyukov, A.V. Medvedev, A.B. Pevtsov, L.M. Sorokin, and J.L. Hutchison. Structural, photonic band-gap, and luminescence properties of the opal–erbium composite. Phys. Solid State 44, 2224–2231 (2002). S.F. Kaplan, N.F. Kartenko, D.A. Kurdyukov, A.V. Medvedev, and V.G. Golubev. Electroluminescent three-dimensional photonic crystals based on opal-phosphor composites. Appl. Phys. Lett. 86, 071108-1-3 (2005). S.F. Kaplan, N.F. Kartenko, D.A. Kurdyukov, A.V. Medvedev, A.G. Badalyan, and V.G. Golubev. Photo- and electroluminescence of sulfide and silicate phosphors embedded in synthetic opal. Photonics Nanostruct. Fundam. Appl. 5, 37–43 (2007). D.A. Mazurenko, R. Kerst, J.I. Dijkhuis, A.V. Akimov, V.G. Golubev, D.A. Kurdyukov, A.B. Pevtsov, and A.V. Sel`kin. Ultrafast optical switching in three-dimensional photonic crystals. Phys. Rev. Lett. 91, 213903-1-4 (2003). D.A. Mazurenko, R. Kerst, A.V. Akimov, A.B. Pevtsov, D.A. Kurdyukov, V.G. Golubev, A.V. Sel`kin, and J.I. Dijkhuis. Femtosecond Bragg switching in opal-a-nc-Si photonic crystals. J. Non-Cryst. Solids 338–340, 215–217 (2004). D.A. Mazurenko, R. Kerst, J.I. Dijkhuis A.V. Akimov, V.G. Golubev, A.A. Kaplyanskii, D.A. Kurdyukov, and A.B. Pevtsov. Subpicosecond shifting of the photonic band gap in a three – dimensional photonic crystal. Appl. Phys. Lett. 86, 041114-1-3 (2005). A.B. Pevtsov, D.A. Kurdyukov, V.G. Golubev, A.V. Akimov, A.A. Meluchev, A.V. Sel`kin, A.A. Kaplyanskii, D.R. Yakovlev, and M. Bayer. Ultrafast stop band kinetics in a 3D opal-VO2 photonic crystal controlled by a photoinduced semiconductor–metal phase transition. Phys. Rev. B 75, 153101-1-4 (2007). A.V. Akimov, Y. Tanaka, A.B. Pevtsov, S.F. Kaplan, V.G. Golubev, S. Tamura, D.R. Yakovlev, and M. Bayer. Hypersonic modulation of light in three-dimensional photonic and phononic band-gap materials. Phys. Rev. Lett. 101, 033902-1-4 (2008). A. Polman. Erbium implanted thin film photonic materials. J. Appl. Phys. 82, 1–39 (1997). V.G. Golubev, V.Yu. Davydov, N.F. Kartenko, D.A. Kurdyukov, A.V. Medvedev, A.B. Pevtsov, A.V. Scherbakov, and E.B. Shadrin. Phase transition governed opal-VO2 photonic crystal. Appl. Phys. Lett. 79, 2127–2129 (2001). V.G. Golubev, J.L. Hutchison, V.A. Kosobukin, D.A. Kurdyukov, A.V. Medvedev, A.B. Pevtsov, J. Sloan, and L.M. Sorokin. Three-dimensional ordered silicon-based nanostructures in opal matrix: preparation and photonic properties. J. Non-Cryst. Solids 299–302, 1062– 1069 (2002). A. Cavalleri, Cs. Tóth, C.W. Siders, J.A. Squier, F. Ráksi, P. Forget, and J.C. Kieffer. Femtosecond structural dynamics in VO2 during an ultrafast solid-solid phase transition. Phys. Rev. Lett. 87, 237401-1-4 (2001). P. Jiang, J.F. Bertone, K.S. Hwang, and V.L. Colvin. Single-crystal colloidal multilayers of controlled thickness. Chem. Mater. 11, 2132–2140 (1999). G.M. Gajiev, V.G. Golubev, D.A. Kurdyukov, A.V. Medvedev, A.B. Pevtsov, A.V. Sel’kin, and V.V. Travnikov. Bragg reflection spectroscopy of opal-like photonic crystals. Phys. Rev. B 72, 205115-1-9 (2005).

MEMS DEVICE AND RELIABILITY PHYSICS

PULL-IN DYNAMICS OF ELECTROSTATICALLY

ACTUATED BISTABLE MICRO BEAMS

1

SLAVA KRYLOV AND NIR DICK

2

1

Microsystems Design and Characterization Laboratory School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, Ramat Aviv, 69978, Israel, e-mail: [email protected] 2 Microsystems Design and Characterization Laboratory School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, Ramat Aviv, 69978, Israel, e-mail: [email protected]

Abstract Bistable micro and nano structures integrated into microsystems exhibit clear functional advantages including the existence of several stable configurations at the same actuation force, extended working range and tunable resonant frequencies. In this work, after a short review of various operational principles of bistable micro devices, we present results of a theoretical investigation of the transient dynamics of an initially curved bistable micro beam actuated by distributed electrostatic and inertial forces. The unique combination of mechanical and electrostatic nonlinearities results in the existence of sequential mechanical (snap-through) and electrostatic (pull-in) instabilities. A phase plane analysis performed using a consistently derived lumped model along with the numerical reduced order model results indicate that the dynamic character of loading may have significant influence on the stability range of the beam. Critical voltages corresponding to the dynamic snap-through and pull-in instabilities are lower than their static counterparts while the minimal curvature required for the appearance of the dynamic snap-through is higher than in the static case.

Keywords: Curved micro beam, electrostatic actuation, dynamic stability, dynamic snapthrough, dynamic pull-in, bistability, phase-plane analysis.

E. Gusev et al. (eds.), Advanced Materials and Technologies for Micro/Nano-Devices, Sensors and Actuators, DOI 10.1007/978-90-481-3807-4_9, © Springer Science + Business Media B.V. 2010

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1. Introduction Many mechanical structures exhibit bistable behavior, namely, the existence of two different stable configurations at the same loading. The transition between two stable states is commonly refereed as a snap-through buckling. The reason for bistability is geometric nonlinearity and a non-monotonous stiffness – deflection characteristic resulting in the stiffening of the structure in the post-buckling configuration, Figure 1a. The analysis of structures liable to snap-through buckling is a wellestablished topic and widely reported in literature [1–3]. Since bistability could be beneficial in micro devices, significant efforts were devoted to development of bistable micro structures. Generally speaking, bistable microstructures could be subdivided into two groups – mechanically bistable and electrostatically bistable structures. 1 Mechanically bistable devices utilize snap-through buckling associated only with mechanical nonlinearity [4–13]. The loading is typically independent of displacement and realized as mechanical force [4] or provided by magnetic [5–7], thermal [8, 9] or electrostatic comb drive actuators [10–12] or kinematic excitation [13]. Electrostatic bistability is related to the nonlinear dependence of the electrostatic force on the deflections. The transition between two stable states is accompanied by an electrostatic pull-in instability arising due to the generic softening influence of the electrostatic force [14]. When the actuating voltage exceeds a pull-in value, the structure collapses on the electrode. However, if a mechanical constraint is provided limiting the displace-

(a)

(b) Force

Electrode

Stopper

Curved beam

Force

Pull-in

Release

Stopper Endpoint deflection

Snap-through

Release

Midpoint deflection

Beam

Voltage

Figure 1. (a) Mechanically bistable structure: arch-shaped beam. (b) Electrostatically bistable structure: cantilever actuated by a close-gap electrode and a stopper limiting the end point deflection. Gray lines represent an additional stable equilibrium, dashed lines correspond to the unstable configurations.

______ 1

Similar considerations are applicable to magnetically bistable structures which are not considered here.

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ment and preventing the contact with the electrode an additional stable equilibrium may exist beyond the pull-in point [15–20] and the system is bistable, Figure 1b. Note that implementation of suspensions with a stiffening force–deflection dependence permits realization of the electrostatic bistability without contact. For example, initially curved microbeam loaded by an electrostatic end force applied along the beam is shown to be bistable in [21]. Pull-in collapse is followed by a straightening of the beam and a steep increase in the mechanical stiffness resulting in an appearance of an additional stable equilibrium. An additional example is a double-clamped straight beam symmetrically actuated by two electrodes [22]. On the other hand, a special arrangement of the electrodes in microactuators may lead to a stiffening rather than softening characteristic of the electrostatic force [23] providing an additional restoring force necessary for the stabilization of the device after pull-in. A bistable tilting micromirror actuated by vertical comb drives was reported in [24]; non-contact electrostatic bistable actuator incorporating slit structures was presented in [25], and the feasibility of multistability in a tilting actuator with multiple close-gap electrodes was theoretically shown in [26]. In all cases, the structures’ suspensions were mechanically linear and bistability appeared only due to the the electrostatic force. In this work we analyze dynamic stability of an initially curved clamped–clamped micro beam actuated by a distributed electrostatic force. The beam is probably the simplest example of the mechanically bistable structure undergoing nonlinear deflection-dependent electrostatic loading (a multistable circular membrane was studied in [27], an electrostatically actuated bistable string was reported in [28]). It was shown theoretically [29, 30] and experimentally [31, 32] that a sufficiently curved electrostatically actuated beam may exhibit sequential snap-through buckling and pull-in instability. The snap-through is followed by a stiffening of the structure and the appearance of an additional stable equilibrium in the post-buckling configuration. Note that interest in this kind of structure is motivated by its functional advantages, mainly in switch-type devices for optical or radio-frequency (RF) applications [33] as well as in micro- and nanomechanical memory devices [34, 35]. Stable deflection of a curved bistable beam is significantly larger and the operational voltages lower than that of a straight beam of similar dimensions. On the other hand, an electrostatically actuated micro beam can be viewed as a kind of benchmark problem, and was intensively investigated (e.g., see reviews [36–38]). Here dynamic snap-through and pull-in instabilities are analyzed mainly for the case of step-function excitation by a suddenly applied voltage. A reduced order model of the device is built using the Galerkin decomposition. A phase plane analysis is performed using a consistently derived single degree of freedom model, the numerical results are obtained using the reduced order model. We show that the presence of two sequential (snap-through and pull-in) instabilities results in rich dynamic behavior of the structure while the response is essentially influenced by an initial curvature of the beam.

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zˆ Electrode

xˆ Anchor

zˆ0 ( xˆ )

hˆ L

g0

V

Anchor

dˆ

Figure 2. Model of an initially curved beam actuated by a distributed electrostatic force.

2. The model of a curved beam We consider an initially curved double clamped prismatic micro beam of length L, with a rectangular cross-section of area A and second moment of area Iy . The beam is made of isotropic±¡linear elastic material with an effective (plane strain) modulus ¢ of elasticity E˜ = E 1 − ν 2 , where ν is Poisson’s ratio. The beam is actuated by an electrode located at a distance g0 from the beam’s ends, Figure 2. The initial shape ˆ 0(xˆ) such that max [z0 (xˆ)] = 1, where hˆ is is described by the function zˆ0 (xˆ) = hz the initial elevation (hats denote dimensional quantities). In addition the beam is subjected to a distributed inertial loading ρ Anz gz (where gz = 9.81 m/s2 ) acting in the zˆ-direction due to an accelerated motion of the support (see [13, 39]). The motion of the beam considered in the framework of the Euler–Bernoulli theory and the shallow arch approximation [40] is described by the non-dimensional differential equation (see [31] for the development) IV

Z1

(2hz00 w0 − w02 )dx(hz000 − w00 ) =

w¨ + cw˙ + w − α 0

β (t) + γ (1) (1 + hz0 (x) − w(x,t))

completed by homogeneous boundary conditions. Here w(x,t) is the non-dimensional deflection, ( )0 = ∂ /∂ x, ( ˙ ) = ∂ /∂ t and non-dimensional quantities used in the formulation are listed in Table 1. We assume linear viscous damping and use parallel capacitor approximation for the electrostatic force. Equation 1, which, for a given initial shape z0 (x), contains five control parameters – h, c, α , β , γ – served as a basis for the dynamic stability analysis of the shallow curved beams. TABLE 1. Non-dimensional quantities used in the development. ˆ 0 Coordinate h = h/g Elevation

x = x/L ˆq ˜ y /ρ AL4 Time t = tˆ EI w = w/g ˆ 0 ˆ 0 b = b/g ˆ 0 d = d/g ∗

α = (g20 A)/(2Iy ) ˆ 4V 2 )/(2EI ˜ y g30 )∗ Deflection β = (ε0 bL ˜ y g0 ) ρ AL4 )/(EI Width γ = (nz gzq ˜ y Thickness c = cL ˆ 2 / ρ AEI

ε0 = 8.854 × 10−12 F/m - permittivity.

Stretching parameter Voltage parameter Inertial loading parameter Damping parameter

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The dynamic behavior of the beam is analyzed using a reduced-order model based on the Galerkin decomposition. Substitution of the approximation w (x,t) ≈ n

∑ qi (t)ϕi (x) (where ϕi (x) are linear undamped eigenmodes of a straight beam [41]

i=1

such that max [ϕi (x)] = 1) into Eq. 1 followed by the usual Galerkin procedure x ⊂[0,1]

yields the system of nonlinear coupled ordinary differential equations (2) Mq¨ + cMq˙ + Bq + 2α h2 z0 T qz0 − T T T e γ α hq Sqz0 − 2α hz0 qSq + α q SqSq = β F + γ F © ª Here, q = q j (t) is the vector of generalized coordinates and ( )T denotes the matrix transpose. The expressions for the elements of the vector z0 = [z0i ], of the diagonal bending stiffness matrix B = [bi j ], of the symmetric stretching related matrix S = [si j ], and of the diagonal mass matrix M = [mi j ] along with the generalized electrostatic force vectors Fe = { fie } can be found in [31]. The vector of generalized © γª R γ inertia force is Fγ = fi where fi = 01 ϕi (x)dx.

3. Model results 3.1. SINGLE DEGREE OF FREEDOM MODEL In order to highlight the leading dynamical phenomena through the analysis of simplified expressions, we first consider the single DOF undamped system (lumped model). We consider the initial shape described by the first mode, i.e., z0 (x) = ϕ1 (x). In addition, we set ϕ1 (x) ≈ (1/2)[1 − cos(2π x)] in the expression for fie and obtain the approximation f1e ≈ (1/2)(1 + h − q)−3/2 (see [42] for a straight beam). In view of the aforementioned, Eq. 2 takes the form

β˜ d2q 2 2 3 ˜ ˜ ˜ p +F(q) = 0 where α h )q − 3 α hq + α q − F(q)=(1 + 2 −γ˜ (3) dτ 2 (1+h−q)3 p γ Here q = q1 , τ = t b11 /m11 , α˜ = α s211 /b11 , β˜ = β /(2b11 ) and γ˜ = γ f1 /b11 . Note γ that for the adopted base functions, b11 = 198.462, s11 = 4.878, m11 = 0.396, f1 = 0.523. One observes that for the constant values of α and h the response of the beam is parameterized by the voltage and the inertial loading parameters β and γ . Fixed points q∗ of Eq. 3 are found from the condition F (q ∗) = 0. Bifurcation diagrams for the case γ = 0 are shown in Figure 3a. One observes that in the case of a sufficiently curved beam, four real roots and two sequential instabilities – snapthrough and pull-in – may exist within the range 0 ≤ q1∗≤ 1 + h. The corresponding values of the deflection and the voltage parameter are denoted qS , βS and qPI , βPI , respectively; qR , βR corresponds to the release (snap-back) configuration (see [31] for the detailed static stability analysis).

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S. KRYLOV AND N. DICK (a)

1

(b)

1

0.9 0.8

0.8

0.6

0.6

0.5

q/(1+h)

q/(1+h)

0.7

0.4

0.4

0.3 0.2

1

2

0 0

(c)

100

0.2

3

0.1

β

200

(d)

0.9 0.8

0 0

300

200

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300

Pull−in

Release

Snap−through

β

q/ (1+h)

β

100

0

0.4

Release

0.3

0.1 0

100

1

200

0.6

0.2

2

Pull−in

0.7

0.5

3

−100

Snap−through

100

200

γ

300

400

−200 0

100

200

γ

300

400

Figure 3. (a) Bifurcation diagram for the curved micro beam for γ = 0 and different initial elevations: 1 – h = 0, 2 – h = 0.35 and 3 – h = 0.45. (b) Bifurcation diagrams for the curved micro beam for h = 0.45 and different values of the inertial loading:1 – g = 0, 2 – g = 100, 3 – g = 150. Solid lines correspond to stable equilibria; dashed lines represent unstable equilibria. (c) Critical deflections and (d) critical values of the voltage parameter for h = 0.45 as a function of the inertial loading parameter. Non-dimensional parameters correspond to the L = 1,000 µm long d = 3 µm thick and b = 30 µm wide beam and g0 = 10 µm.

The influence of the inertial loading is illustrated in Figure 3b–d. The support is assumed to move at a constant acceleration while actuation voltage increases quasistatically (see [39] for the shock loading). One observes that while the presence of acceleration results in a decrease of the critical voltages, its influence on the snapthrough voltage is more pronounced. Note that the meaning of a negative β is that the electrostatic force acts in the direction opposite to the inertial loading. The conclusions about the nature of the fixed points are made based on the eigenvalue analysis of Eq. 3 linearized around the fixed points. The eigenvalues λ1,2 = ±iλ are pure imaginary for q∗ < qS and qR < q∗ < qPI (the fixed point is a center), λ1,2 = 0 for q∗ = qS or q∗ = qPI (cusp) and λ1 < 0, λ2 > 0 for qS < q∗ < qR or qPI < q∗ < 1 + h (saddle). Figure 4a, b illustrate the dependence of λ on q ∗ and the voltage parameter β , respectively. Due to the bistability of the beam, the frequency may have two different values at the same actuation voltage. One observes also that the frequency can be efficiently tuned by the voltage in a very large range.

PULL-IN DYNAMICS OF BISTABLE MICRO BEAMS (a)

2

(b)

1

λ

λ

1

1.5

1

2

2

2 0.5 0

2 2

1

1.5

123

0.5

0

0.2

0.4

0.6

q/(1+h)

0.8

0

1

0

50

100

β

150

200

250

Figure 4. Eigenvalue λ of Eq. 3 linearized around the fixed points q∗ for the case of a straight beam h = 0 (curve 1) and an initially curved beam for h = 0.35 (curve 2). The fundamental frequency of the initially curved unloaded beam is higher than of the straight beam.

The snap through and pull-in instability are dynamic phenomena and cannot be described by the quasi-static approach. In order to illustrate the influence of the dynamic character of loading, we consider a beam subject to a voltage suddenly applied at t = 0 (i.e., β (t) = β H(t) where H(t) is the Heaviside step function), zero initial conditions q(0) = 0, q˙(0) = 0 and in absence of the inertial loading γ = 0. Calculating first integral of Eq. 3 we obtain 1 2 where U = (1 + 2α˜ h2 )

µ

dq dτ

¶2

= H −U

(4)

q2 q4 2β˜ − α˜ hq3 + α˜ − √ 2 4 1+h−q

(5)

is the √potential energy and H is Hamiltonian (for zero initial conditions, H = −2β˜ / 1 + h). The trajectories on the phase plane, Figure 5a, the solution along a trajectory, Figure 5b and the non-dimensional period T are given by the expressions

p dq = ± 2(H −U) dτ

Z qmax

Zqmax

τ= 0

dq p 2(H −U)

T =2

p 0

dq 2(H −U)

(6)

One observes that in the case of a moderately curved beam the behavior is similar to a straight beam: step-function excitation by a voltage lower than the dynamic pull-in value β < βDPI results in a periodic motion around a stable node on the phase plane. An increase in the voltage beyond the dynamic pull-in, which corresponds to the separatrix on the phase plane, results in dynamic instability and divergent motion.

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5

5 4

5

4

2

3

1

h= 0.45

h= 0.35

h= 0.3

3 4

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5

2

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3

4

3

3

2

1

5

3

1

2 5 4

Figure 5. Influence of an initial elevation h on the dynamic responses of the bell-shaped beam subjected to a suddenly applied voltage: (a) phase plane trajectories and (b) time histories. Different curves correspond to different actuation voltages:1 – β < βDS ; 2 – β = βDS < βS ; 3 – β = βS ; 4 – β = βDPI < βPI ; 5 – β = βPI . Non-dimensional parameters correspond to the L = 1000 µm long d = 3 µm thick and b = 30 µm wide beam and g0 = 10 µm. Some trajectories cannot be reached under zero initial conditions.

For higher values of the initial elevation, dynamic snap-through may occur (the corresponding voltage parameter is denoted βDS ) in addition to the dynamic pullin. In this case the phase plane contains two separatrices. The first one is a homoclinic connection emerging from a saddle corresponding to the dynamic snapthrough. Within each of two stable regions “low amplitude” periodic motion is possible around stable nodes corresponding to two stable equilibrium configurations. The second separatrix corresponds to the dynamic pull-in instability. In the case βDS < β < βDPI , a “high amplitude” periodic motion is possible around two stable nodes corresponding to the two stable configurations before and after the snapthrough. 2 At larger values of the initial elevation, βDS > βDPI and the phase plane contains two separatrices corresponding to the dynamic snap-through and dynamic pull-in. It was shown in [31] that, under quasi-static operation, the relative initial elevation h/d should be higher than a certain value in order to reach the snap-through buckling. Phase plane analysis suggests that the minimal initial elevation required for the appearance of the dynamic snap-through is higher that in the static case. As

______

2

At some specific value of the initial elevation, βDS = βDPI and two separatrices corresponding to the dynamic snap-through and the dynamic pull-in may merge into one trajectory combining homoclinic and heteroclinic connections.

Pull−in

Dyn. pull−in

200

0.6

Pull−in

β

q/(1+h)

0.8

Dyn.pull−in

0.4

Dyn.snap−through

150 Snap−through

0.2

0 0

Dyn. sn ap−thro

(b) 250

(a) 1

125

ugh

PULL-IN DYNAMICS OF BISTABLE MICRO BEAMS

Snap−through 0.1

0.2

0.3

h

0.4

0.5

0.6

100 0

0.1

0.2

0.3

h

0.4

0.5

0.6

Figure 6. Critical values of the displacement (a) and the voltage parameter (b) corresponding to the snap-through, pull-in, dynamic snap-through and dynamic pull-in. Non-dimensional parameters correspond to the 1,000 µm long, 3 µm thick beam, the distance to electrode is g0 = 10 µm. One observes that dynamic snap through appears at higher elevations than static snap-through while the dynamic critical voltages are lower than their static counterparts.

a result, a situation is possible when the beam is bistable under the static operation but the dynamic snap-through is not present. Note that the suppression of the snap-through under dynamic operation was reported in [29] where an electrostatically actuated curved beam was analyzed numerically using a combination of finite elements and boundary elements methods. The results of the present work, obtained by means of the phase-plane analysis, provide an explanation for this kind of behavior and present a quantitative estimation of the initial curvature required for the appearance of dynamic snap-through. Figure 6 illustrates the location of the critical points, in terms of deflections and actuation voltages, corresponding to the static and dynamic snap-through and pull-in instabilities. One observes that the interval of the initial elevation exists where the beam is statically bistable but the dynamic snap-through is suppressed.

3.2. NUMERICAL RESULTS Finally we present numerical results obtained using the RO model. The system of Eq. 2 was solved numerically using the solver ode15s integrated into Matlab package. In all cases, the parameters of the beam used in calculations were L = 1,000 µm, dˆ = 3 µm, distance to electrode g 0 = 10 µm. The response was obtained using the RO model with five base functions. The responses of an undamped and damped micro beam undergoing a suddenly applied voltage are presented in Figure 7a, b respectively. In the damped system decaying vibrations around one of two stable equilibrium configurations are

S. KRYLOV AND N. DICK

Midpoint deflection (µm)

(a) 14 5

12 10 8

4

6

3

4 2

2 0 0

(b)

14

Midpoint deflection (µm)

126

12

1

50

100

Time (µs)

150

10 8 4

6

3

4 2

2 0 0

200

5

1

50

100

150

Time (µs)

200

Figure 7. (a) Time history for the undamped micro beam in the case of a step function actuation. Different curves correspond to different applied voltages: 1 − V = 110 V; 2 − V = 116.1 V < VDS ; 3 −V = 116.3 V > VDS ; 4 −V = 120 V < VDPI ; 5 −V = 121.8 V > VDPI . (b) Time history for the damped beam: 1 −V = 110 V ; 2 −V = 120 V < VDS ; 3 −V = 120.3 V > VDS ; 4 −V = 122 V < VDPI ; 5 −V = 126 V > VDPI . The initial elevation is hˆ = 3.85 µm, quality factor is Q = 10.

(b) 14

14 12 10

4

Midpoint deflection (µm)

Midpoint deflection (µm)

(a)

3

8 6

2

4 2 0 0

1

50

100

Time (µs)

150

200

12

3

4

2

10

1

8 6 4 2 0 0

50

100

Time (µs)

150

200

Figure 8. (a) Time history for the undamped micro beam in the case of a step function actuation and hˆ = 3.2 µ m. Different curves correspond to different applied voltages: 1 −V = 100 V ; 2 −V = 110 V ; 3−V = 123 V < VDPI ; 4−V = 125 V > VDPI . (b) Time history in the case of a ramp function actuation and maximal voltage of VS < 125 V < VPI . Different curves correspond to different time of the voltage increase: 1 −t0 = 100 µ s; 2 −t0 = 95 µs; 3 −t0 = 50 µs; 4−step function excitation. Dashed lines represent the damped response corresponding to the quality factor Q = 10. Gray lines schematically illustrate the character of the applied voltage.

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observed, depending on the applied voltage. Similarly to the case of a straight beam, dynamic snap-through and dynamic pull-in voltages in the damped system are consistently higher than in the undamped case. Figure 8a illustrates undamped response of a beam with the initial elevation h = 0.32. Since the beam does not exhibit dynamic snap-through under zero initial conditions, no large amplitude low frequency motion in the vicinity of the separatrix is observed (compare Figure 7a, curve 3). Influence of the dynamic character of the loading is illustrated in Figure 8b. In this loading scenario, the voltage V (tˆ) = V0tˆ/tˆ0 increases linearly for tˆ ≤ tˆ0 and remains constant for tˆ > tˆ0 . One observes that the snap-through instability is suppressed for t0 smaller that a certain value (see [29]) and dynamic pull-in instability followed by divergent motion is observed.

Acknowledgements The research is supported by The Israel Science Foundation (Grant No. 1426/08).

References 1. Simitses GJ (1989) Dynamic stability of suddenly loaded structures. Springer-Verlag, New York 2. Singer J, Arbocz J, Weller T 1(998–2002) Buckling experiments: experimental methods in buckling of thin-walled structures. Wiley, Chichester New York 3. Timoshenko SP, Gere JM (1961) Theory of elastic stability. 2nd ed McGraw-Hill 4. Qui J, Lang JH, Slocum AH (2004) A curved beam bistable mechanism. J Microelectromech Syst 13:137–146 5. Vangbo M, B¨acklund Y (1998) A lateral symmetrically bistable buckled beam. J Micromech Microeng 8:29–32 6. Han JS, Ko JS, Kim YT, Kwak BM (2002) Parametric study and optimization of a microoptical switch with a laterally driven electromagnetic microactuator. J Micromech Microeng 12:939–947 7. Seunghoon P, Dooyoung H (2008) Pre-shaped buckled-beam actuators: Theory and experiments. Sens Act A: Phys 148:186–192 8. Michael A, Kwok CY (2006) Design criteria for bi-stable behavior in a buckled multi-layered MEMS bridge. J Micromech Microeng 16:2034–2043 9. Qui J, Lang JH, Slocum AH, Weber AC (2005) A bulk-micromachined bistable relay with U-shaped thermal actuators. J Microelectromech Syst 14:1099–1109 10. Saif MTA (2000) On a tunable bistable MEMS – theory and experiment. J Microelectromech Syst 9:157–170 11. Sulfridge M, Saif T, Miller N, Meinhart M (2004) Nonlinear dynamic study of a bistable MEMS: model and experiment . J Microelectromech Syst 13:725–731 12. Casals-Terre´ J, Fargas-Marques A, Shkel AM (2008) Snap-action bistable micromechanisms actuated by nonlinear resonance. J Microelectromech Syst 17:1082–1093 ´ E, Collard D (2007) Post-buckling dynamic behavior of self13. Buchaillot L, Millet O, Quevy assembled 3D microstructures. Microsyst Technol 14:69–78 14. Pelesko JA, Bernstein DH (2002) Modeling of MEMS and NEMS. Chapman&Hall A CRC Press Company, London New York Washington DC 15. Gorthi S, Mohanty A and Chatterjee (2006) A Cantilever beam electrostatic MEMS actuators beyond pull-in. J Micromech Microeng 16:1800–1810 16. Hung ES, Senturia SD (1999) Extending the travel range of analog-tuned electrostatic actuators. J Microelectromech Syst 8:497–505

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17. Krylov S and Barnea D (2005) Bouncing mode electrostatically actuated scanning micromirror for video applications. Smart Mater Struct 14:1281–1296 18. Krylov S, Maimon R (2004) Pull-in dynamics of an elastic beam actuated by continuously distributed electrostatic force. J Vib Acoust 126:332–342 19. McCarthy B, Adams GG, McGruer NE, Potter DA (2002) Dynamic model, including contact bounce, of an electrostatically actuated microswitch. J Microelectromech Syst 11:276–283 20. Zhang J, Zhang Z, Lee YC, Bright VM, Neff J (2003) Design and investigation of multilevel digitally positioned micromirror for open-loop controlled applications. Sens Act A: Phys 103:271–283 21. Krylov S and Bernstein Y (2006) Large displacement parallel plate electrostatic actuator with saturation type characteristic. Sens Act A: Phys 130131:497–512 22. Elata D and Abu-Salih S (2005) Analysis of a novel method for measuring residual stress in micro-systems. J Micromech Microeng 15:921–927 23. DeMartini BE, Rhoads JF, Turner KL, Shaw SW, Moehlis J (2007) Linear and nonlinear tuning of parametrically excited MEMS oscillators. J Microelectromech Syst 16:310–318 24. Hah D, Patterson PR, Nguyen HD, Toshiyoshi H, Wu MC (2004) Theory and experiments of angular vertical comb-drive actuators for scanning micromirrors. IEEE J Sel Top Quantum Electron 10:505–513 25. Lee KB (2007) Non-contact electrostatic microactuator using slit structures: theory and a preliminary test. J Micromech Microeng 17:2186–2196 26. Shmilovich T, Krylov S (2009) A single-layer tilting actuator with multiple close-gap electrodes. J Micromech Microeng 18 (in press) 27. Pelesko JA, Chen XY (2003) Electrostatically deflected circular elastic membranes. J Electrostat 57:1–12 28. Krylov S, Seretensky S (2006) Higher order corrections of electrostatic pressure and its influence on the pull-in behavior of microstructures. J Micromech Microeng 16:1382–1396 29. Das K, Batra RC (2009) Pull-in and snap-through instabilities in transient deformations of microelectromechanical systems. J Micromech Microeng 19: pap 035008 30. Krylov S, Seretensky S (2006) (2006) Pull-in and multistability analysis of an initially curved beam. in Digest Tech Papers Asia-Pacific Conf of Transducers and Micro-Nano Technol APCOT 2006, Singapore, June 25–28 2006, pap D-27 31. Krylov S, Ilic BR, Schreiber D, Seretensky S, Craighead H (2008) Pull-in behavior of electrostatically actuated bistable microstructures. J Micromech Microeng 18: pap 055026 32. Zhang Y, Wang Y, Li Z, Huang Y, Li D (2007) Snap-through and pull-in instabilities of an arch-shaped beam under an electrostatic loading. J Microelectromech Syst 16:684–693 33. Rebeiz GM (2003) RF MEMS : theory, design, and technology. Wiley-Interscience, Hoboken NJ 34. Charlot B, Sun W, Yamashita K, Fujita H, Toshiyoshi H (2008) Bistable nanowire for micromechanical memory. J Micromech Microeng 18:1–7 35. Tsai Chun-Yin, Kuo Wei-Ting, Lin Chi-Bao, Chen Tsung-Lin (2008) Design and fabrication of MEMS logic gates. J Micromech Microeng 18:pap 045001 36. Batra RC, Porfiri M, Spinello D (2007) Review of modeling electrostatically actuated microelectromechanical systems. Smart Mater Struct 16: R23-R31 37. Fargas-Marques A, Costa CR, Shkel AM (2005) Modelling the electrostatic actuation of MEMS:state of the art 2005. Technical Report. 38. Nayfeh AH, Younis MI, Abdel-Rahman EM (2005) Reduced-order models for MEMS applications. Nonlin Dyn 41:211–236 39. Younis MI, Alsaleem F, Jordy D (2007) The response of clampedclamped microbeams under mechanical shock. Int J Non-Lin Mech 42:643–657 40. Villagio P (1997) Mathematical models for elastic structures. Cambridge Univ Press, Cambridge 41. Blevins RD (1979) Formulas for natural frequency and mode shape. Van Norstrand Reinhold, New York 42. Pamidighantam S, Puers R, Baert K, Tilmans HAC (2002) Pull-in voltage analysis of electrostatically actuated beam structures with fixedfixed and fixedfree end conditions. J Micromech Microeng 12:458–64

PATH FOLLOWING AND NUMERICAL CONTINUATION METHODS FOR NON-LINEAR MEMS AND NEMS

1

2

PETER G. STEENEKEN AND JIRI STULEMEIJER 1

NXP-TSMC Research Center, NXP Semiconductors, HTC 4, 5656 AE Eindhoven, the Netherlands, E-mail: [email protected] 2 Epcos Netherlands, 6546 AS Nijmegen, The Netherlands, E-mail: [email protected]

Abstract Non-linearities play an important role in micro- and nano-electromechanical system (MEMS and NEMS) design. In common electrostatic and magnetic actuators, the forces and voltages can depend in a non-linear way on position, charge, current and magnetic flux. Mechanical spring structures can cause additional non-linearities via material, geometrical and contact effects. For the design and operation of non-linear MEMS devices it is essential to be able to model and simulate such non-linearities. However, when there are many degrees of freedom, it becomes difficult to find all equilibrium solutions of the non-linear equations and to determine their stability. In this paper a generic methodology to analyze MEMS devices using path following methods is described. Starting from the energy and work expressions of electromechanical systems (Section 1), the equations of motion, the equilibrium and stability conditions are derived (Sections 2, 3 and 6). The basics of path following are introduced in Section 4. Using several examples it is discussed how path following can be implemented in Mathematica, M ATCONT and in the FEM package C OMSOL (Sections 5–8).

Keywords: Non-linear MEMS, capacitive MEMS, finite-element method.

1. Energy and work in electromechanical systems In this paper a generic methodology to analyze the static equilibria of MEMS and NEMS is discussed, which can be summarized as follows: • Determine the expressions for internal energy and work. • Derive the equations of motion and equilibrium conditions using the Hamilton equations. • Start from an initial equilibrium state and determine the other states and their stability using path following.

E. Gusev et al. (eds.), Advanced Materials and Technologies for Micro/Nano-Devices, Sensors and Actuators, DOI 10.1007/978-90-481-3807-4_10, © Springer Science + Business Media B.V. 2010

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MEMS and NEMS devices can usually be treated using classical physics in the quasistatic electromagnetic approximation, if the system dimensions are small compared to the electromagnetic wavelength and are large enough to neglect quantum effects. In these approximations the total internal energy of the system Utot = ∑ U and total work done by external sources Wtot = ∑ W can be expressed as a sum over different types of energy and work, given by Eqs. 1–10:

Ukin = Ugrav =

Z Z

V

V

p2m,i 1 1 p2m dV ≈ ∑ 2 ρm 2 i mi

(1)

1 G 1 VG ρe dV ≈ ∑ mi ∑ m j 2 2 i r j ij

!

! 1 1 −1 J · AdV ≈ ∑ Φi ∑ Li j Φ j Umag = 2 i V 2 j ! Z 1 1 V ρe dV ≈ ∑ Qi ∑ Ci−1 Uel = j Qj 2 i V 2 j ! Z 1 1 Ustrain = ε · σ dV ≈ ∑ xi ∑ ki j x j 2 i V 2 j Z

Wkin = Wgrav = Wmag = Wel = Wstrain =

Z Z pm V

0

Z Z ρm V

0

Z Z A V

0

0

Z Z ε V

0

i

Z pm,i

VG,ext dρm dV ≈ ∑ i

Jext · dAdV ≈ ∑ i

Z Z ρe V

vext · dpm dV ≈ ∑

Vext dρe dV ≈ ∑ i

σ ext · dε dV ≈ ∑ i

0

Z xi 0

Z Φi 0

Z Qi 0

Z xi 0

vext,i dpm,i

mi gext,i dxi

(2) (3) (4) (5) (6) (7)

Iext,i dΦi

(8)

Vext,i dQi

(9)

Fext,i dxi

(10)

The expressions are given to show that there is a striking similarity between energy and work equations in different physical domains. As a result of this, their physics can be analyzed by the same mathematical methods. The energy and work expressions in each of the equations can be written in terms of continuum volume V integrals over energy densities. As shown on the right side, the integrals can also be approximated by sums over lumped or finite elements which can be treated numerically by finite element methods. Note that the expressions in Eqs. 1–5 are only valid in the linear regime, intrinsic non-linearities can modify the expressions. The variables in Eqs. 1–10 are given as follows. ρm is the mass density, pm is the mass momentum density. VG is the gravitational potential and G is the gravitational constant. V is the electric potential, ρe is the charge density, J is the total current

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density and A is the magnetic vector potential. σ and ε are the mechanical stress and strain. The expressions on the right side of the equations are written as sums over discrete charges Qi , magnetic fluxes Φi and masses mi at positions xi and with mass momentum pm,i , which are coupled via effective springs k ij , gravitational potential G/ri j , capacitors Ci j and inductors Li j . The components of the inverse capacitance and inductance matrices C−1 and L−1 relate potential to charge −1 V j = ∑i Ci−1 j Qi and relate current to magnetic flux I j = ∑i Li j Φi . The total work Wtot supplied to the system is a sum of the work from external gravitational VG,ext , current density Jext , electric Vext , magnetic Aext and stress σ ext fields. The kinetic work term Wkin is needed to account for a relative speed difference vext between the frame of reference of the system and the frame of the observer. The work can also be performed on discrete elements by external gravitational acceleration gext,i , current Iext,i or voltage Vext,i sources or external (stress) forces Fext,i . For more details on Eqs. 1–10 the reader can refer to standard texts on classical mechanics and electromagnetics. External thermal sources at temperature Text , which add heat Qh to the system, can be treated by similar methods, although this requires keeping track of the entropy S and temperature T in the system. According to the first lawR of thermodynamics (dUtot = δ Qh + δ Wtot ), this requires adding an integral Qh = 0S Text dS to the work equations. The internal thermal energy of the material is in essence a sum of the kinetic energy R R of the atoms which can be expressed by a thermal energy term Utherm,kin = V 0T c(T )ρm dT dV , where c(T ) is the specific heat capacity. The work provided by Ran electrical Rsource in Eq. 9 can be rewritten using integration by parts: W el = V (Vext ρe − 0Vext ρe dV ext ) dV . It is often convenient to define the coenergyR or complementary energy as the Legendre transform of the R R work such that Uel∗ ≡ V Vext ρe dV − Wel = V 0Vext ρe dVext dV . Figure 1 shows how energies and coenergies can be represented graphically for a voltage controlled capacitive MEMS switch example which is treated in Section 5 and Figure 3. This figure shows how a consideration of the energy and work in a system can provide insight and additional information compared to a consideration of the forces only. Moreover, as will be shown in the next section, transduction mechanisms between different physical domains, like the electrostatic force, can be derived from the energy and work expressions.

2. Equations of motion and energy conservation The Hamiltonian H is the difference between the total internal energy Utot and the total supplied work Wtot . It can be described by a set of generalized coordinates qi with (i = 1 , . . ., N) and corresponding generalized momenta pi : H (q1 , . . . , qN , p1 , . . . , pN ) = Utot − Wtot

(11)

From the Hamilton equations the generalized forces Fi and speeds vi are given by:

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Figure 1. Energy and coenergy diagrams of a voltage controlled capacitive MEMS switch. Left: The solid black line represents the static equilibrium states of a capacitive MEMS switch which will be calculated in Section 5. The areas represent the internal electric energy Uel , strain energy Ustrain and coenergy Uel∗ = Vext Q −Wel . Right: If the device is voltage controlled, it will follow the arrows at the pull-in Vpi and release Vre voltage. As a result work Wel will be converted to kinetic energy during pull-in Ukin,close and similarly strain energy from the spring will be converted to kinetic energy Ukin,open at release. The sum of both energies Ukin,close + Ukin,open is the dissipated energy during one switching cycle. Thus energy diagrams constructed from static simulations can provide information on the dynamics and dissipation of the device.

Fi = p˙i =

−∂ H ∂H , vi = q˙i = ∂ qi ∂ pi

(12)

The total internal energy Utot in the system equals the total work Wtot done on the system and therefore the Hamiltonian H , which is the difference between internal energy and work H = Utot − Wtot , is conserved. This follows from the Hamilton equation 12 because:   dH ∂H ∂H =∑ (13) q˙i + p˙i = 0 dt ∂ qi ∂ pi i Let us choose as generalized mechanical coordinates the position qmech,i = xi with as corresponding generalized momentum pmech,i = pm,i , and for the generalized electromagnetic coordinates the charge qem,i = Qi with the magnetic flux pem,i = Φi as corresponding generalized momentum. −1 If the parameters ki j , L−1 i j and Ci j are constants, applying the Hamilton equations 12 to Eqs. 1–11 gives the equations of motion: Fmech,i = p˙m,i = − ∑ ki j x j + mi gext,i + Fext,i , vmech,i = x˙i = pm,i /mi

(14)

−1 ˙ Fem,i = Φ˙ i = − ∑ Ci−1 j Q j + Vext,i , vem,i = Qi = ∑ Li j Φ j + Iext,i

(15)

j

j

j

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This gives us Newton’s second law, Hooke’s law and Faraday’s law of electromagnetic induction. However, if for example the spring constants, inductance and capacitance pa−1 rameters ki j , L−1 i j and Ci j depend on the mechanical positions xi , which is often the case in electromechanical systems, the mechanical and electromagnetical problems become coupled and the mechanical forces become: Fmech,i = − ∑ ki j x j − j

1 ∂ ki j 1 ∂ Ci j 1 ∂ Li j Φi Φ j (16) xi x j − ∑ Qi Q j − ∑ ∑ 2 i, j ∂ xi 2 i, j ∂ xi 2 i, j ∂ xi −1

−1

+mi gext,i + Fext,i This shows that if the parameters depend on xi the generalized mechanical force Fmech,i becomes the sum of coupling forces from different physical domains, like the spring force, electrostatic and magnetostatic forces. In equilibrium this sum of coupling forces is zero. A similar equation applies for the generalized voltage Fem,i .

3. Electromechanical equilibrium The system is defined to be in electromechanical equilibrium if all generalized forces Fi are zero. In equilibrium, the gradient of the Hamiltonian is therefore also zero as shown by Eqs. 17 and 18: −∂ H =0 ∂ qi   ∂H ∂H =0 F = −∇q H = − ,..., ∂ q1 ∂ qN Fi = p˙i =

(17) (18)

For a specific set of generalized momenta pi and generalized external parameters Fgen = {mgext , Fext ,Vext , Iext }, Eq. 17 gives N generalized force equations with N unknowns which can be solved to obtain the equilibrium state of the system. If the energy function has only one variable parameter F and all other parameters are fixed, the equilibrium state q eq,0 at F = F0 thus satisfies: F(qeq,0 , F0 ) = −∇q H (qeq,0 , F0 ) = 0

(19)

Often equilibria exist for which all generalized speeds vi are zero. These equilibria are called static equilibria or stationary states. The equilibrium solutions of a non-linear system can be found using a powerful mathematical technique, which is called path following or numerical continuation [1, 5].

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4. Path following and numerical continuation methods Finding all equilibrium states of an electromechanical system is a difficult problem that cannot be solved in general because it requires one to check the whole N dimensional coordinate space for solutions of Eq. 17, for each value of the external parameters Fgen and momenta pi . However, when an equilibrium solution of the Eq. 17 is known for a certain set of parameters pi , Fgen , it is possible to efficiently find additional solutions using numerical path following techniques [1, 5]. Recently it has been shown that path following techniques can be very useful for the analysis of electrostatic MEMS devices with non-linear contact forces [12]. The technique can in fact be applied to almost any non-linear electromechanical system described by energy equations 1–10. Alternatively, it can be directly applied without the energy equations if the equilibrium conditions (19) are known. In MEMS and NEMS devices, the system is usually controlled by a single external parameter F , which can for example be the voltage or current from an external source for electromechanical actuators, but can also be an acceleration or gas pressure force in sensor systems. The 1-dimensional external parameter F with the N-dimensional coordinate space q form a (N + 1)-dimensional space. The implicit function theorem implies [1, 5] that if one equilibrium solution qeq,0 with F(qeq,0 , F0 ) = 0 exists at external parameter value F0 , then it has to be part of a continuous 1-dimensional equilibrium solution curve qeq (F ) at parameter values F in (N + 1)-dimensional space with qeq,0 = qeq (F0 ). It is therefore often possible to start at a known equilibrium solution qeq (F0 ) and determine the other solutions by following the curve (qeq (F ), F ). Path following methods usually employ a predictor-corrector algorithm [1] to follow an equilibrium curve. In the predictor step, a new solution is predicted, usually by taking a step in the direction of the tangent to the solution curve. In the corrector step, the predicted point is brought back on the solution curve, usually by an iterative method. For the predictor step the tangent direction to the solution curve can be determined as follows. Let us assume that there exists an infinitesimal vector tangent to the solution curve dqeq,0 (dF0 ), with a corresponding infinitesimal parameter change dF0 such that there is another equilibrium state at (qeq (F ), F ) = (qeq,0 + dqeq,0 , F0 + dF0 ). Because the new state should also satisfy Eq. 18 the predictor algorithm can determine the tangent direction vector (dqeq, 0 , dF0 ) in N + 1 dimensional space by solving the N equations: F(qeq,0 + dqeq,0 , F0 + dF0) − F(qeq,0 , F0 )

(20)

= JF(qeq,0 ,F0 ) dqeq,0 = −HH (qeq,0 ,F0 ) dqeq,0 = 0 Where JF(qeq,0 ,F0 ) is the Jacobian of F at (qeq,0 , F0 ). HH is the Hessian matrix of the Hamiltonian, which is the Jacobian of the gradient of the Hamiltonian. Besides the tangent direction, the predictor algorithm also needs to specify the steplength of the vector. The curve (q eq (s),F (s)) can be parametrized by a parameter s, such that the steplength is given by |(∂ q eq /∂ s, ∂ F /∂ s)| × ∆ s. If parameter

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continuation is used, the parameter s is proportional to the external parameter such that s = α F , this however leads to problems when two equilibrium solutions exist at the same value of F . In the commonly used pseudo-arclength continuation algorithm, the parameter s is parametrized by the length along the curve R s = 0s α |(∂ qeq /∂ s, ∂ F /∂ s)|ds such that the steplength is always finite. Note that in order to use path following methods to obtain equilibrium solutions, it is required to start from an initially known equilibrium solution. It is therefore essential that an initial solution can be found, this can sometimes be difficult since there is no general efficient method to find these initial solutions.

5. Example of path following method As an example of the methodology discussed in Sections 1–4 we consider the problem of finding the equilibra of a voltage controlled capacitor connected to a spring from its energy and work equations. A schematic picture of this system is shown in Figure 2.

Figure 2. An electrostatically actuated capacitor of which one plate is connected to a spring.

The system has two generalized coordinates x and Q. The internal energy and work of the system can be used to derive the Hamiltonian: 1 Q2 (g − x) H = Ustrain + Uel − Wel = kx2 + − 2 2Aε0

Z Q 0

Vext,eq (Qeq )dQeq

(21)

Note that for the conservation of H to be valid, it is necessary that the external voltage Vext,eq (Qeq ) is applied such that the system is always in equilibrium along the path, otherwise the kinetic energy of the system would become non-zero. In other words, the path following method will determine the function Vext,eq (Qeq ) which satisfies this condition. The generalized force vector F is found from the gradient of the Hamiltonian:

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F = −∇H = − =



∂H ∂H , ∂x ∂Q



(22)

Q2eq Qeq (g − xeq) −kxeq + ,Vext,eq (Qeq ) − 2Aε0 Aε0

!

=0

The Hessian matrix of the Hamiltonian is found1 to be:

−HH (xeq ,Qeq ) = JF = −

∂ 2H ∂ x2 ∂ 2H ∂ Q∂ x

, ,

∂ 2H ∂ x∂ Q ∂ 2H ∂ Q2

!

=

−k , Qeq A ε0

,

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−

(g−xeq ) A ε0

!

(23)

Figure 3. This script in Mathematica shows how the Veq − Q curve of an electrostatically actuated MEMS switch with a non-linear exponential spring contact can be obtained using path following as described in Section 5 and Figure 2. The spring energy is given by 1 2 2 kx + exp (c1 (x − g + δ )), the electrical energy is Q2 /2C and the capacitance C = Aε0 /(g − x), with k = g = Aε0 = 1, c1 = 100 and δ = 0.1. The path is followed starting from the solution x = V = Q = 0. The Veq − Q curve is identical to that in Figure 1. The x − Q curve is also plotted.

Thus by applying the matrix (23) on the infinitesimal vector (dxeq , dQeq ) along the equilibrium path, Eq. 20 gives us: −HH (dxeq , dQeq ) = (24) Qeq Qeq (g − xeq) ∂ Vext,eq (−kdxeq + dQeq , dxeq + dQeq ) = 0 dQeq − Aε0 Aε0 ∂ Qeq Aε0 Dividing these two equations by dQeq and taking the limit gives after rearranging:

______

1

Alternatively the generalized voltage constraint Qeq = Ceq Vext, eq from Eq. 22 can be used to eliminate the charge degree of freedom as was done in [12].

PATH FOLLOWING AND NUMERICAL CONTINUATION METHODS

Qeq dxeq = dQeq kAε0 Q2eq dVext,eq 1 = − 2 2 dQeq C kA ε0

137

(25) (26)

At an equilibrium point at coordinate (xeq , Qeq ,Vext,eq ) Eqs. 25 and 26 provide dx dVext,eq the tangent vector to the solution curve ( dQeqeq dQeq , dQeq , dQ dQeq ). In Figure 3 eq we show how the equations in this section can be implemented in a Mathematica [10] script to determine the V − Q curve of an electrostatically actuated MEMS switch with a non-linear exponential spring contact (note that the exponential function is only an approximation, see e.g. [13] for a more accurate function). In this example we have used the NDSolve function in Mathematica to follow the solution path solely from the tangent vector function, without using a corrector method. The different types of energy in this system are shown in Figure 1. Dedicated interactive numerical path following packages [8] like M ATCONT [9] and AUTO [2] include corrector methods and stability analysis. They are therefore more robust and convenient to treat complex problems (see Section 7).

6. Stability The system is in a static equilibrium state qeq when the sum of all forces is zero and all generalized momenta are zero. This equilibrium is only stable if for all possible infinitesimal displacement vectors dqeq , the Hamiltonian increases such that H (qeq + dqeq ) > H (qeq ). Any displacement would therefore violate the conservation of energy and thus the system will remain in state qeq forever. The local Taylor expansion of the Hamiltonian is given by: 1 H (q + dq) = H (q) + ∇H (q) · dq + dq · HH (q)dq 2

(27)

At a static equilibrium point, the gradient of H is zero according to Eq. 19, so the system is stable if the right term of Eq. 27 is positive for all dq. The vector dq can be written as dq = ∑Ni adq,i qˆ H,i , where qˆ H,i are the eigenvectors of the Hessian matrix with corresponding eigenvalues λ i. Therefore in Eq. 27 the term 21 dq·HH (q) dq = 12 ∑Ni λi a2dq,i qˆ 2H,i , is always positive if all eigenvalues λi of the Hessian matrix are positive (the Hessian matrix is positive definite). Points at which λi = 0 are called folds or bifurcations. At bifurcations there is more than one solution dqeq,0 of Eq. 20. Since these zero crossings of λ i cause a sign change of an eigenvalue, the stability of the system usually changes at these points. Note that the Hessian matrix used in Eq. 27 for stability determination can be different from that for path following in Eq. 24. As an example, to determine the stability of an equilibrium condition under voltage control, the voltage Vext,eq is kept constant, such that in this case ∂ Vext,eq / ∂ Qeq = 0 in Eq. 21. It is found that in this example the stability changes at

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(xeq = g/3) at which the determinant of the matrix is zero, because the determinant is the product of all eigenvalues. If the charge Q ext on the device in Section 5 is kept constant, no work is done such that Wel = 0. It is found that xeq = Q2ext /2kAε0 is always stable (det H = k). 1 0.9

LP LP

H

0.8 0.7

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Figure 4. Left: Model equations in M ATCONT for two identical uncoupled switches with the same parameters as the switch in Figure 3. Right: Calculated equilibrium curves. Folds (LP) and bifurcations (H) are automatically detected by the software. The folds (LP) correspond to the pull-in and release instabilities of one switch, at bifurcations (H) both switches are unstable for pull-in or release.

7. Numerical path following in MATCONT As an example of the use of M ATCONT for path following, we take two identical uncoupled switches with the same parameters as in Figure 3 and enter the force and momentum equations (12) as shown on the left side of Figure 4. To improve convergence of the calculation a mass and damping term have been added to the force equations. On the right side of Figure 3 the calculated path following curves are shown. Path following programs like M ATCONT monitor the eigenvalues of the Hessian on the equilibrium path to determine the stability of the system and plot the folds (LP) and bifurcation points (H) as shown in Figure 4. As an example two identical capacitive MEMS switches are simulated in in Figure 4. All eigenvalues of the Hessian are positive on the line from (0,0)-H. At the bifurcation point H ( 13 , 31 ), two eigenvalues become zero and both switches become unstable towards pull-in. On the paths H-LP only one switch is unstable and the other is open (one negative eigenvalue), on the path H-H both switches are unstable (two negative eigenvalues). On segments LP–LP between the release and pull-in point of one of the switches and on the segment H-(1,1), where both switches are closed, the system is stable and all eigenvalues are positive. More details on path following simulations of two uncoupled switches can be found in [12].

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8. Finite element method path following simulations The examples given up to now have a low number of degrees of freedom, such that their energy equations can be entered manually. To model continuous systems, for which the energy and work equations are given by the volume integrals in Eqs. 1–10, dedicated finite element method (FEM) software is available. These packages mesh the volume and construct partial differential equations that provide the equations of motion for all degrees of freedom. Moreover they provide efficient solvers, such that systems with thousands or even millions of degrees of freedom can be solved.

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Figure 5. Simulation of the equilibria of a voltage actuated single clamped Euler beam (adapted from [12]). (a) The capacitance voltage curve shows two pull-in (A,C) and two release (B,D) instabilities. The pull-in voltage at point A corresponds to the transition from no contact (float) to contact with a single point (pinned). The pull-in at point C corresponds to the transition from single point contact (pinned) to contact over a finite length (flat). The stable equilibria are indicated by solid lines and the unstable by dotted lines. (b) The displacement shape of the beam at 5 points (A–E) on the C −V curve.

Some finite element packages do provide basic path following methods to solve non-linear problems, however the control over the followed path and the detection of stability is less advanced than in the dedicated path following packages [8] discussed in the previous section. To analyze non-linear MEMS systems with path following methods in a FEM package (for more examples see [3, 6, 12]), we have written a script for C OMSOL [4]. The script is similar to that presented in [11] and predicts the initial condition for the next calculation and uses the solver of C OMSOL as a corrector. The prediction direction is a linear extrapolation based on the two previous solutions. The predicted steplength is based on the previous steplength and the curvature of the path. The obtained corrected solution is discarded if its direction or distance is too far from the predicted point. Since C OMSOL provides direct access to the stiffness matrix k = −HH , the stability of the solutions can be determined by checking the sign of the eigenvalues of this matrix. By making use of the stiffness matrix, more sophisticated predictor algorithm scripts can be developed.

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In Figure 5 an example of a FEM simulation of a voltage actuated single clamped beam is shown, which was obtained using the C OMSOL script. The results correspond well to the analytical results in [7]. More details and examples of FEM numerical path following can be found in [12]. Although this example is still relatively simple, the FEM path following method can theoretically be applied to analyze any non-linear system of which the Hamiltonian H can be written in terms of the Eqs. 1–10.

9. Conclusions A generic methodology to analyze the static equilibria of MEMS and NEMS has been discussed. It was shown that path following can be a powerful mathematical tool to determine the equilibrium solutions of electromechanical systems and their stability from the energy and work expressions. The path following of the electromechanical equilibrium solutions can be performed by analytical methods, dedicated numerical software or finite element method software.

References 1. Allgower, E.L. and Georg, K.: Numerical path following. In: Cialet, P.G., Lions, J.L. (eds.) Handbook of Numerical Analysis 5, pp. 3207. Elsevier, Amsterdam (1997) 2. AUTO , http://indy.cs.concordia.ca/auto/ 3. Batra, R. C., Porfiri, M. and Spinello, D.: Analysis of Electrostatic MEMS Using Meshless Local Petrov-Galerkin (MLPG) Method. Engineering Analysis with Boundary Elements, 30, 949–962 (2006) 4. C OMSOL, http://www.comsol.com 5. Doedel, E.J.: Lecture Notes on Numerical Analysis of Nonlinear Equations. In: Krauskopf, B., Osinga, H.M. and Galn-Vioque, J. (eds.) Numerical Continuation Methods for Dynamical Systems, pp. 1–49. Springer, Dordrecht (2007) 6. Gerson, Y., Krylov, S., Ilic, B. and Schreiber, D.: Large displacement low voltage multistable micro actuator. In: Proc. IEEE MEMS 2008, pp. 463–466 (2008) 7. Gorthi, S., Mohanty, A. and Chatterjee, A.: Cantilever beam electrostatic MEMS actuators beyond pull-in. J. Micromech. Microeng., 16, 1800–1810 (2006) 8. Govaerts, W. and Kuznetsov, Y.A.: Lecture Notes on Numerical Analysis of Nonlinear Equations. In: Krauskopf, B., Osinga, H.M. and Galn-Vioque, J. (eds.) Numerical Continuation Methods for Dynamical Systems, pp. 51–76. Springer, Dordrecht (2007) 9. M ATCONT, http://www.matcont.ugent.be 10. Mathematica, http://www.wolfram.com/ 11. M¨oller J.: Bifurcation analysis using C OMSOL multiphysics. In: Proc. Nordic C OMSOL Conf., pp. 1541–1544 (2006) 12. Stulemeijer, J., Bielen, J.A., Steeneken, P.G. and van den Berg, J.B.: Numerical Path Following as an Analysis Method for Electrostatic MEMS. J. Microelectromech. Systems, 18, 488–499 (2009) 13. Suy, H.M.R., Herfst, R.W., Steeneken, P.G., Stulemeijer, J. and Bielen J.A.: The static behavior of RF MEMS capacitive switches in contact. In: Proc. NSTI Nanotech 2008 Vol. 3, pp. 517–520 (2008)

THE IMPACT OF DIELECTRIC MATERIAL AND TEMPERATURE ON DIELECTRIC CHARGING IN RF MEMS CAPACITIVE SWITCHES

GEORGE PAPAIOANNOU Solid State Physics Section, Physics Department, University of Athens, Panepistimiopolis Zografos, Athens 15784, Greece, E-mail: [email protected]

Abstract The present work attempts to provide a better insight on the dielectric charging in RF-MEMS capacitive switches that constitutes a key issue limiting parameter of their commercialization. The dependence of the charging process on the nature of dielectric materials widely used in these devices, such as SiO2, Si3N4, AlN, Al2O3, Ta2O5, HfO2, which consist of covalent or ionic bonds and may exhibit piezoelectric properties is discussed taking into account the effect of deposition conditions and resulting material stoichiometry. Another key issue parameter that accelerates the charging and discharging processes by providing enough energy to trapped charges to be released and to dipoles to overcome potential barriers and randomize their orientation is the temperature will be investigated too. Finally, the effect of device structure will be also taken into account.

Keywords: Dielectrics, charging, RF MEMS.

1. Introduction The dielectric charging constitutes a major problem that still inhibits the commercial application of RF MEMS capacitive switches. The effect arises from the presence of the dielectric film (Figure 1) and macroscopically is manifested through the shift [1–4] or/and narrowing [5, 6] of the pull-in and pull-out voltages window thus leading to stiction and device failure. The first qualitative characterization of dielectric charging within capacitive membrane switches and the impact of high actuation voltage upon switch lifetime were presented by C. Goldsmith et al. in [7] who reported that the dependence of number of cycles to failure on the peak actuation voltage follows an exponential relationship [7]. Particularly it was reported that the lifetime improves by an order of a decade for every 5 to 7 V decrease in applied voltage. Presently it is well known that the commonly quoted number of cycles to failure does not constitute a good measure of the reliability of switches suffering from charging. W.M. van Spengen et al. [8] have shown that E. Gusev et al. (eds.), Advanced Materials and Technologies for Micro/Nano-Devices, Sensors and Actuators, DOI 10.1007/978-90-481-3807-4_11, © Springer Science + Business Media B.V. 2010

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number of cycles to failure is severely affected by the actuation frequency and duty cycle. Further they have shown that since the failure is purely due to charging, the contact time (down position gives rise to charge injection) is equal for all. Since the cycling method does not provide essential information on the failure mechanisms, the investigation on dielectric charging was extended by involving MIM (Metal–Insulator–Metal) capacitors to determine the stored charge, charging and discharging times constants as well as the [3, 9] as well as to monitor the various charging mechanisms [10], since these devices approximate MEMS switches in the pull-down state. Another method that approximates more precisely the charging through asperities and surface roughness in MEMS is the Kelvin Probe Force Microscopy. This method has been employed to investigate the charging and discharging through the measurements of the dielectric film surface potential [11, 12].

Figure 1. Simplified model of a capacitive switch based on parallel plate model.

The dielectric charging occurs independently of the actuation scheme and the ambient atmosphere [5]. Up to now the effect has been attributed to the charge injection during the pull-down state [2, 4, 6, 13] and dipoles orientation [12–14], which are present in the dielectric material. In order to minimize and control the dielectric charging and obtain devices with high capacitance aspect ratio, several materials, such as SiO2 [3], Si3N4 [4, 14], AlN [17, 18], Al2O3 [19, 20], Ta2O5 [21], HfO2 [22, 23], have been used. The selection has been made taking into account the maturity of low temperature deposition method and the magnitude of dielectric constant. Although these materials exhibit excellent insulating properties little attention was paid on the fact that their lattice is formed by either covalent or ionic bonds, which affect significantly the dielectric polarization/charging. It is worth noticing that among these materials, the crystalline AlN exhibits piezoelectric properties, which seems to increase significantly the device lifetime [19].

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A key issue parameter that affects significantly the electrical properties of dielectrics and may prove to constitute a valuable tool for the determination of device lifetime is the device operating temperature. This is because temperature accelerates the charging [14–16, 24] and discharging [25] processes by providing enough energy to trapped charges to be released and to dipoles to overcome potential barriers and randomize their orientation. Finally, the presence or absence [26] of dielectric film as well as its expansion on the film on the insulating substrate [27] constitute a key issue parameter that influences the charging process. The aim of the present work is to attempt to provide a better understanding of the impact of the material properties on the dielectric charging. The basic polarization mechanisms in dielectrics will be presented in order to obtain a better insight on the effect of the ionic or covalent bonds of the dielectrics used in capacitive MEMS. The deviation from stoichiometry, due to low temperature deposition conditions, will be taken into account. Finally, the effect of temperature on the charging and discharging processes will be discussed in order to draw conclusions on the possibility of identification and predict of charging mechanisms and their relation to the deposition conditions.

2. Polarization/charging mechanisms The polarization of a solid dielectric submitted to an external electric field occurs through a number of mechanisms involving microscopic or macroscopic charge displacement. According to the time scale of polarization build up we can divide the polarization mechanisms in two categories, the instantaneous and the delayed time dependent polarization. The instantaneous polarization mechanisms, which play no important role in MEMS, consist of: The electronic polarization which is the fastest process requiring about 10−15 s and results from the deformation of the electronic shell The atomic polarization requiring about 10−14 to 10−12 s and results from the atomic displacement in molecules with heteropolar bonds constituting another deformation process The other polarization mechanisms [28–32], which are responsible for the “dielectric charging” effects are characterized by a time constants that may be as low as 10−12 s or as large as years, so that no relaxation is observed under the conditions of observation. These mechanisms are called slow and may occur through a number of processes involving either microscopic or macroscopic charge displacement. The slow polarization mechanisms, a summary of which is presented in Figure 2, are as follows: The dipolar or orientational polarization occurs in materials containing permanent molecular or ionic dipoles. In this mechanism depending on the frictional resistance of the medium, the time required for this process can vary between picoseconds to even years. The dipolar polarization of inorganic crystals may be caused by structural properties of the crystal lattice or it may be due to

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lattice imperfection or doping, for example in impurity vacancy dipole systems. The structural interpretation of the dielectric processes occurring in many polar materials is usually approached by assuming impaired motions or limited jumps of permanent electric dipoles. In molecular compounds for example, relaxation can be considered as arising from hindered rotation of the molecule as a whole, of small units of the molecule or some flexible group around its bond to the main chain, while in ionic crystals, it can be mainly associated with ionic jumps between neighboring sites (ion-vacancy pairs). From conventional dielectric measurements it is known that materials obeying the classical Debye treatment with a single relaxation time are rather rare.

(a)

(b)

Figure 2. Summary of polarization mechanisms under (a) non contacting and (b) contacting charging.

The space charge or translational polarization is observed in materials containing intrinsic free charges such as ions or electrons or both. The space charge polarization arises from macroscopic charge transfer towards the electrodes that may act as total or partial barriers. Moreover, the charging of space-charge electrets may be achieved by injecting (depositing) charge carriers. Other methods consist in the generation of carriers within the dielectric by light, radiation or heat and simultaneous charge separation by a field. The space charge polarization causes the material to be spatially not neutral (Figure 2) hence is a much more complex phenomenon than the dipolar polarization. The interfacial polarization, which sometimes is referred as Maxwell– Wagner–Sillars (MWS) polarization, is characteristic of systems with heterogeneous structure. It results from the formation of charged layers at the interfaces due to unequal conduction currents within the various phases. In structurally heterogeneous materials, such as complicated mixtures or semi-crystalline products, it can be expected that field-induced ionic polarization will obey more closely an interfacial model of the Maxwell–Wagner–Sillars type than a space-charge model of the barrier type [33]. There the action of an electric field can achieve a migration charge by (a) bulk transport of charge carriers within the higher conductivity phase and (b) surface migration of charge carriers. As a consequence surfaces, grain boundaries, interphase boundaries (including the surface of precipitates) may charge. Charges “blocked” at the interface between two phases with different

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conductivity give a contribution to the net polarization of the body exposed to the electric field. In most of the theoretical treatments, the polarized material is assumed to be free of charge carriers, so that the internal field and the dipolar polarization can be considered as space independent. In practice, however, dipolar and space charge polarizations often coexist and the electric field and polarization must then be considered as averaged over the thickness of the sample. Finally, the simultaneous displacement of free charges and dipoles during the polarization process may lead to a particular situation where the internal electric field is nearly zero, so that no preferred orientation of dipoles occurs.

3. Material considerations As already mentioned the dielectric materials used in MEMS capacitive switches are as SiO2, Si3N4, AlN, Al2O3, Ta2O5 and HfO2. The charging mechanisms in each dielectric will depend on the material structure and for this reason each one will be discussed separately. So far the dielectric charging has been intensively investigated in SiO2 and Si3N4. Regarding the other materials i.e. Ta2O5, HfO2 and AlN there is little information on their impact on the reliability of MEMS devices. In the case of Ta2O5 [21] and HfO2 [22, 23], although the materials are attractive due to their large dielectric constant, the knowledge on the charging processes is still limited and arises from the study of MIM and MIS capacitors, the latter for MOSFET gate applications. Both materials exhibit ionic conduction and in the case of Ta2O5 it has been shown that under high electric field space charge arises due to formation of anodic–cathodic vacancy pair, (Frenkel pair dissociation) [35]. Moreover, isothermal current transients in chemical vapor deposited material revealed that protons are incorporated in the structure and the current transient arises from proton displacement [36]. For HfO2 it has been shown that hole trapping produces stable charge [37]. The trapped charge density was found to be strongly sensitive on the deposition methods and the work-function of the gate electrodes. In thin layers (≤10 nm) it was shown that charge trapping follows a logarithmic dependence on time [38]. On the other hand the detrapping rate was found to depend on the film thickness, with a power law behavior as a function of time. α-Al2O3 is a wide-gap insulator with a direct energy gap of about 8.3 eV [39]. The O–Al bonds in the compound exhibit highly ionic nature and theoretical calculations have shown that the valence band is well separated into two parts, with the lower part consisting of O 2s states and the upper part being dominated by O 2p states. The lower part of the conduction band is in general believed to be dominated by Al 3s states. Regarding the electrical properties and charging behavior the dc behavior of alumina has been little investigated. The experimental I(t) curves have shown that the ‘quasi’ steady-state current is reached for time ranging from 104 to 105 s [40]. The transient current was reported to consist of two

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parts, the first one that arises mainly from the polarization of dipoles in the dielectric which dominate at short time, whereas the second part was found to correspond to the carriers transport mechanism. Moreover the conduction mechanism in the high field regime was reported to obey the space charge limited current law. The conduction mechanism high temperatures has been found to be dominated by carriers emitted from deep traps while the low temperatures one by carriers emitted from discrete shallow traps or transport in the band tails [41, 42]. Here it must be pointed out that the characteristics of the charge traps introduced during deposition depend strongly on the deposition conditions [41]. Aluminum nitride (AlN) piezoelectric thin film is very popular in RF micromachined resonators and filters MEMS devices. The advantages arise from its high resistivity and piezoelectric coefficient, which is the largest among nitrides as well as the possibility to be deposited at temperatures as low as 500°C and patterned using conventional photolithographic techniques. AlN generally exhibits smaller piezoelectric and dielectric constant and differs from PZT materials in that it is polar rather than ferroelectric. Theoretical results have indicated that nitride semiconductors possess a large spontaneous polarization [42], associated with which are electrostatic charge densities analogous to those produced by piezoelectric polarization fields. In wurtzite structure the polar axis is parallel to the c-direction of the crystal lattice that may give rise to a macroscopic spontaneous polarization, which can reach values up to 0.1 C/m2. This macroscopic lattice polarization is equivalent to two dimensional fixed lattice charge densities with values between 1013 and 1014 e/cm2 located at the two surfaces of a sample [43]. Finally, in inhomogeneous alloy layers, variations in composition are expected to create non-vanishing and spatially varying spontaneous and piezoelectric polarization fields and associated charge densities that can significantly influence the material properties. Thus in contrast to the single crystalline material, the sputtered one exhibit near-zero, positive or even negative piezoelectric response indicating a change in crystalline orientation, grain size, concentration of defects or even a complete reversal of dipole orientation [43, 44]. Recently, AlN has been introduced in MEMS switches [45] and reliability tests have proved that under low pull-in bias or certain polarity the device degradation may be extremely low. Assessment of MIM capacitors with crystalline AlN dielectric has indicated that this behavior has to be attributed to the presence of a spontaneous polarization arising from dislocations that may induce a surface charge of the order of 6.6 × 10−7 C/cm2, which is much smaller than the theoretically predicted spontaneous polarization [18]. The SiO2 and Si3N4 are the most important dielectrics used in modern siliconbased electronic devices. In spite of the five decades of intensive investigation, the gained knowledge has not be effectively applied in MEMS capacitive switches. The reasons behind this deficiency lie on the fact that in MEMS capacitive switches technology the dielectric film is deposited on rough metal surfaces at low temperatures (≤300°C). Thus the film surface morphology is affected by the substrate and the low temperature leads to significant deviation of stoichiometry. The latter allows us to describe silicon oxide and nitride as SiOx and and SiNx

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with x < 2 and x < 1.33 respectively. The low temperature deposition gives rise to formation of silicon nanoclusters and/or nanocrystals in both materials due to the fact that Si excess is high and the phase separation mechanism is not nucleation and growth as in the case of low Si excess, but spinodal decomposition [48]. Figure 3a shows clearly the percolation of nanocrystal after 1 min annealing at 1,000°C under Ar ambient. A simplified schematic diagram illustrating the twodimensional structure of SiNx [49] shows in Figure 3b (bottom) the regions of silicon phase, stoichiometric silicon nitride, and subnitrides and (top) the corresponding energy band profile. Similar is the behavior of SiOx [50, 51].

(a)

(b)

Figure 3. (a) Cross-sectional energy-filtered TEM image of Si-ncs embedded in SiNx layers deposited with a gas flow that corresponded to 21% Si excess [48] and (b) representation of material non-homogeneity and band gap fluctuation [49].

Although these materials consist of covalent bonds, in substoichiometric silicon oxide the Eδ' defect gives rise to the formation of dipoles by trapping holes [52]. Although these dipoles were observed after gamma ray irradiation, their presence in the SiOx used in MEMS capacitive switches cannot be overruled. Moreover, the presence of such structures cannot be rejected in SiNx. Taking all these into account we can conclude that the charging mechanisms taking place in insulating films used in MEMS capacitive switches can be summarized in Table 1. So, in all cases the space charge polarization due to presence of free charges or injected charges as well as the dipolar polarization constitutes the major charging mechanisms. The presence of nanoclusters or nanocrystals is expected to give rise to a random distribution of dipolar polarization and in the same time is expected to give rise to interfacial polarization; a fact that needs to be experimentally demonstrated. Presently, due to above analyzed effects, there is still no clear information on the charging of thin dielectric films used in MEMS capacitive switches. The electrical properties of these dielectrics obviously depend strongly on the deposition

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methods and conditions. Due to the absence of standardization of deposition methodology, the study of dielectric charging, employing MEMS and MIM devices, still leads to no concrete results. A key issue parameter, towards the solution of this problem, seems to be the dielectric film temperature since it accelerates the charging and discharging processes by providing enough energy to trapped charges to be released and to dipoles to overcome potential barriers and randomize their orientation. The effect of temperature will be analyzed in the following. TABLE 1. Charging mechanisms. Material SiO2 Si3N4 Al2O3 AlN HfO2 Ta2O5

Ionic – – D D D D

Dipolar (D) (D) D D D D

Space charge D D D D D D

(D) Due to deviation from stoichiometry.

4. Effect of temperature In insulators, the time and temperature dependence of polarization and depolarization processes are, in the case of dipolar polarization, determined by the competition, between the orienting action of the electric field and the randomizing action of thermal motion. In the case of space charge polarization the processes are far more complex because several mechanisms can be involved simultaneously [29]. In spite of these, the charging and discharging process time constant is thermally activated described by τ (T ) = τ 0 exp ⎛⎜ E A ⎞⎟ . This allows us to plot the depend-

⎝ kT ⎠

ence of room temperature normalized relaxation time constant on activation energy of relaxing mechanism (Figure 4a). Here it must be pointed out that the time constant normalization has been performed with respect to time constant at 450 K, which is considered for the sake of simplicity is assumed to be τ 450 K = 1 . This dependence has been demonstrated through thermally stimulated depolarization current measurements on MIM capacitors with SiNx materials deposited under different conditions [53, 54] (Figure 4b) In the case of MEMS switches, the pull-up transient is affected by to persisting electrostatic force due to dielectric charging. Thus the fast mechanical response is followed by a slow transient which is corresponds to the dielectric film discharging process. The discharge transient was found to follow the stretched β ⎡ ⎤ exponential relaxation law Δ C (t ) = Δ C 0 exp ⎢ − ⎛⎜ t ⎞⎟ ⎥ [25] (Figure 5a), where β ⎢⎣ ⎝ τ ⎠ ⎥⎦

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is the stretch factor (0 ≤ β ≤ 1) that indicated the deviation from the Debye law and τ the process relaxation, which dependence on temperature has been described above. The recording of pull-up transient as a function of temperature allows us to draw the Arrhenius plot and determine the process activation energy hence to determine the “signature” of the corresponding discharging mechanism or mechanisms in the case there are several [25] (Figure 5b). Here it must be emphasized that the activation energy allows us to predict the behavior of a charging/ discharging mechanisms through the Arrhenius plot. If further the investigation is extended on materials deposited with different methods and/or conditions, the sensitivity of the activation energy on the deposition conditions will allow us to draw conclusions on the nature of the charging mechanism. 6

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The transient itself provides information only on the activation energy of charging mechanism. The nature of the dominant charging mechanism i.e. dipolar or space charge polarizations, the latter arising from charge injection or intrinsic free charges, can be only obtained from the shift of the bias at minimum of z σ capacitance-voltage characteristic, V min = − d , where σ is the average

ε0

value of equivalent surface charge, zd the dielectric film thickness and ε0 the vacuum dielectric constantan. Drawing both the Arrhenius and shift of Vmin with temperature in the same figure allows us to determine the activation energy and charge origin of each contributing mechanism (Figure 5b).

G. PAPAIOANNOU

0.14

10

10

0

10

5 0

-1

10

0V -40V

-5

-2

1

10

t

[sec] (a)

10

[x10-8C/cm2]

0.16 0.15

1

[sec]

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15

0.54eV

0.45eV

T = 310K

τ

COFF

[pF]

0.18

2.2

2.4

2.6

2.8

1000/T

3.0

3.2

σ

150

3.4

[K]

(b)

Figure 5. (a) Pull-up transient and (b) simultaneous drawing of Arrhenius plot and shift of Vmin [25].

5. Conclusions The present work attempted to provide a better insight on the dielectric charging in RF-MEMS capacitive switches. It was shown that the dielectric material properties play a key issue role in the dielectric charging process. It was shown that in ionic materials the ionic/dipolar polarization as well as the space charge polarization is the dominant charging mechanisms. In the case of the well established SiNx and SiOx dielectric materials the covalent bonds prevent the dipolar polarization. On these materials are Si-rich and the significant deviation from stoichiometry gives rise to the formation of Si nanoclusters and nanocrystals which in turn allows the formation of defects that exhibit dipole properties, hence giving rise to dipolar polarization in addition to the space charge one. The dependence of both polarization mechanisms on temperature allows drawing conclusions on the nature of charging mechanisms. This can be achieved by monitoring both the Arrhenius plots of discharging or charging mechanisms as well as the polarity of the dielectric film equivalent surface charge.

References 1. 2. 3.

Rebeiz, G. M., “RF MEMS,” in Theory, Design and Technology. Hoboken, NJ: Wiley, 2003, pp. 185–192 J. Wibbeler, G. Pfeifer and M. Hietschold, Parasitic charging of dielectric surfaces in capacitive microelectromechanical systems (MEMS), Sensors and Actuators A 71, 74–80 (1998) X. Yuan, S. Cherepko, J. Hwang, C. L. Goldsmith, C. Nordquist and C. Dyck, Initial Observation and Analysis of Dielectric-Charging Effects on RF MEMS Capacitive Switches, International Microwave Symposium, pp. 1943–1946, 2004

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10. 11.

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21. X. Rottenberg, H. Jansen, P. Fiorini, W. De Raedt, H. A. C. Tilmans, “Novel RF-MEMS capacitive switching structures”, 32nd European Microwave Conference, 1–4, 2002. 22. J.K. Luo, M. Lin, Y.Q. Fu, L. Wang, A.J. Flewitt, S.M. Spearing, N.A. Fleck, W.I. Milne, “MEMS based digital variable capacitors with a high-k dielectric insulator”, Sensors and Actuators A 132 (2006) 139–146 23. J. Tsaur, K. Onodera, T. Kobayashi, Z.-J. Wang, S. Heisig, R. Maeda, T. Suga , “Broadband MEMS shunt switches using PZT/HfO2 multi-layered high k dielectrics for high switching isolation”, Sensors and Actuators A 121 (2005) 275–281 24. R. Daigler, G. Papaioannou, E. Papandreou and J. Papapolymerou, “Dielectric Charging in RF-MEMS Capacitive Switches - Effect of Dielectric Film Thickness”, International Microwave Symposium 1275–8, 2008 25. G. Papaioannou, E. Papandreou, J. Papapolymerou, R. Daigler, “Dielectric Discharging processes in RF-MEMS Capacitive Switches”, Asia-Pacific Microwave Conference, 2007. APMC 1–4, 2007 26. D. Mardivirin, A. Pothier, A. Crunteanu, B. Vialle and P. Blondy, IEEE Trans. on Microwave Theory and Tech. 57, 231 (2009) 27. P. Czarnecki, X. Rottenberg, P. Soussan, P. Ekkels, P. Muller, P. Nolmans, W. De Raedt, H.A.C. Tilmans, R. Puers, L. Marchand, I. DeWolf, “Effect of substrate charging on the reliability of capacitive RF MEMS switches”, Sensors and Actuators A in press 28. J. van Turnhout in: G.M. Sessler (Ed.) Topics in Applied Physics: “Electrets”, vol. 33, ch. 3, pp. 81–216, Springer-Verlag, Berlin, 1987 29. J. Vandershueren and J. Casiot, Topics in Applied Physics: Thermally Stimulated Relaxation in Solids, P. Braunlich, Ed. Berlin, Germany: Springer-Verlag, 1979, vol. 37, ch. 4. 30. E. Barsoukov and J. Ross Macdonald, “Impedance Spectroscopy Theory, Experiment, and Applications”, John Wiley & Sons, Inc., Hoboken, New Jersey, 2005 31. Kwan Chi Kao, “Dielectric Phenomena in Solids, With Emphasis on Physical Concepts of Electronic Processes”, Elsevier Academic Press 2004 32. C.J.F. Böttcher, “Theory of electric polarization”, Elsevier, Amsterdam 1952 33. V. V. Daniel, “Dielectric Relaxation” (Academic Press, New York, 1967) 34. A. Toriumi, K. Tomida, H. Shimizu, K. Kita and K. Kyuno, Far- and mid-infrared absorption of HfO2/SiO2/Si system, in Silicon Nitride, Silicon Oxide Thin Insulating Films and Other Engineering Dielectrics VIII, by R. E. Sah et al. editors, 471–481, 2005 35. S. Duenas, H. Castan, J. Barbolla, R.R. Kola, P.A. Sullivan, Electrical characteristics of anodic tantalum pentoxide thin ®lms under thermal stress, Microelectronics Reliability 40 (2000) 659±662 36. K.-H. Allers, P. Brenner, M. Schrenk, Dielectric reliability and material properties of Al2O3 in metal insulator metal capacitors (MIMCAP) for RF bipolar technologies in comparison to SiO2, SiN and Ta2O5, Proceedings of the Bipolar/BiCMOS Circuits and Technology Meeting, 2003, 35–38, 2003 37. M. Strømme Mattsson and G. A. Niklasson, Isothermal transient ionic current as a characterization technique for ion transport in Ta2O5, J. of Applied Physics 85, 8199–8204, 1999 38. V.V. Afanas’ev, A. Stesmans, Injection induced charging of HfO2 insulators on Si, Materials Science and Engineering B 109 (2004) 74–77 39. G. Puzzilli and F. Irrera, Long time transients in hafnium oxide, Microelectronic Engineering 84 (2007) 2394–2397 40. C M Fang and R A de Groot, “The nature of electron states in AlN and α-Al2O3”, J. Phys.: Condens. Matter vol. 19 pp. 386223 1–6, 2007 41. F. Talbi, F. Lalam and D. Malec, “DC conduction of Al2O3 under high electric field”, J. Phys. D: Appl. Physics vol. 40, pp. 3803–3806, 2007 42. Cheng Rong Li, Li Jian Ding, Jin Zhuang Lv, You Ping Tu and Yang Chun Cheng, “The Relation of Trap Distribution of Alumina with Surface Flashover Performance in Vacuum”, IEEE Trans. on Dielectrics and Electrical Insulation vol. 13, pp. 79–84, 2006

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43. E. Papandreou, A. Crunteanu, G. Papaioannou, P. Blondy, F. Dumas-Bouchiat, C. Champeaux and A. Catherinot , Investigation of dielecric charging mechanisms in Al2O3 RF mems capacitive switches, MEMSWAVE 2008, Herakleio Crete 44. F. Bernardini, V. Fiorentini, and D. Vanderbilt, “Spontaneous polarization and piezoelectric constants of III-V nitrides”, Phys. Rev. B 56 (1997), R10024-7. 45. A. Zoroddu, F. Bernardini, P. Ruggerone and V. Fiorentini, “First-principles prediction of structure, energetics, formation enthalpy, elastic constants, polarization, and piezoelectric constants of AlN, GaN, and InN: Comparison of local and gradient-corrected densityfunctional theory” Physical Review B 64 (2001), 045208-1–045208-6 46. J.A. Ruffner, P.G. Clem, B.A. Tuttle, D. Dimos and D.M. Gonzales, “Effect of substrate composition on the piezoelectric response of reactively sputtered AlN thin films”, Thin Solid Films 354 (1999), 256–261 47. M. Stutzmann et al., “Playing with polarity”, Physica Status Solidi (b) 228 (2001), 505–512 48. T. Lisec, C. Huth and B. Wagner, Dielectric Material Impact on Capacitive RF MEMS Reliability, 12th GAAS Symposium European Microwave Week, 471–4, 2004 49. M. Carrada, A. Zerga, M. Amann, J.J. Grob, J.P. Stoquert, A. Slaoui, C. Bonafos, S. Scham, Structural and optical properties of high density Si-ncs synthesized in SiNx:H by remote PECVD and annealing, Materials Science and Engineering B 147 (2008) 218–221 50. V. A. Gritsenko, D. V. Gritsenko, Yu. N. Novikov, R. W. M. Kwok and I. Bello, Shortrange order, large scale potential fluctuations and photoluminescence in amorphous SiNx, Journal of Experimental and Theoretical Physics, Vol. 98, No. 4, 2004, pp. 760–769 51. F. Iacona, C. Bongiorno, C. Spinella, Formation and evolution of luminescent Si nanoclusters produced by thermal annealing of SiOx films, J. of Applied Physics 95, 2004, 3723 52. K. Yoshida, I. Umezu, N. Sakamoto, M. Inada and A. Sugimura, Effect of structure on radiative recombination processes in amorphous silicon suboxide prepared by rf sputtering, J. of Applied Physics 92, 2002, 5936 53. D. M. Fleetwood et al., Dipoles in SiO2: Border traps or not?, in Silicon Nitride, Silicon Oxide Thin Insulating Films and Other Engineering Dielectrics VII, by R. E. Sah et al. editors, 291, 2003 54. E. Papandreou, M. Lamhamdi, C.M. Skoulikidou, P. Pons, G. Papaioannou and R. Plana, Structure dependent charging process in RF MEMS capacitive switches, Microelectronics Reliability 47, pp. 1812–1817, 2007

ADVANCED PROCESSES AND MATERIALS

DEVELOPMENT OF DRIE FOR THE NEXT GENERATION OF MEMS DEVICES

H. ASHRAF, J. HOPKINS AND L.M. LEA SPP Process Technology Systems UK Limited, Imperial Park, Newport, UK, E-mail: [email protected]

Abstract This paper describes methods to increase the aspect ratio of features whilst maintaining a high throughput using DRIE technology. The component parts of the Bosch process are considered with the aim to increase the efficiency of each step. By controlling process parameters within a cycle and cycle to cycle, etch rate and aspect ratio can be increased.

Keywords: DRIE (deep reactive ion etching), HAR (high aspect ratio), MEMS, silicon, parameter ramping.

1. Introduction The Bosch process [1] has been fundamental in enabling the commercialisation of MEMS devices. Before this pioneering technique, plasma processing used a mixture of gases in a continuous mode to etch material. This proved to have limitations on etch rate and selectivity. To limit isotropic etching, the lateral etch rate has to be inhibited at the same time as maintaining vertical etching. This would typically involve having high bias to enable the feature base to be kept free of etch inhibitors whilst simultaneously protecting the sidewalls from etching. Examples of such processes are BCl3/Cl2 used in GaAs etching [2] and SF6/O2 used in Si etching [3]. The process parameters (gas flow rates and composition, ICP coil power, bias power and pressure) are used to control the profile and etch rate. For the commercialisation of MEMs devices in silicon, the Bosch process or DRIE (deep reactive ion etching) has become the mainstay for the majority of applications due to its’ versatility. The process consists of three parts; deposition, removal of deposition at the feature base and etch (Figure 1). This cyclical approach enables anisotropic features to be etched in silicon with higher etch rates and increased selectivities compared to the continuous non switched technique (Table 1). The downside to the Bosch approach is that the switched cyclical nature gives rise to sidewall roughness or “scallops” however with optimization of the process recipe this effect can be minimised. In this paper, each aspect of the DRIE process is considered with the aim of developing the process for the next generation of devices where higher throughputs and increased aspect ratio are essential. E. Gusev et al. (eds.), Advanced Materials and Technologies for Micro/Nano-Devices, Sensors and Actuators, DOI 10.1007/978-90-481-3807-4_12, © Springer Science + Business Media B.V. 2010

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(a)

(b)

(c)

Figure 1. Schematic of the Bosch Process (DRIE) (a) deposition of CFx layer; (b) removal of deposition; (c) etching of silicon. TABLE 1. Comparison of Bosch and continuous mode processes for silicon etching [3–6]. Continuous

DRIE

Typical etch rates (µm/min)

1–10

4–50

Typical selectivity

18 µm/min)

Figure 7. SEMS of features demonstrating the advantage of using parameter ramping.

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Dep

Etch

Dep

Etch

Pressure (a) Bias

Time

Pressure (b)

Low pressure/high bias for deposition removal

Bias

Time Pressure

Pressure decreasing

High pressure to maintain etch rate

(c)

Bias

Bias increasing Time

Figure 8. Schematic for ramping technique: (a) basic Bosch technique; (b) changing parameters within cycle; (c) changing parameters within cycle and cycle to cycle.

4. Conclusion In order to increase throughput for the DRIE process, each step of the process needs to be optimised for efficiency; this requires the maximisation of the chemical etch for silicon, ensuring the maximum deposition rate to increase the etch:deposition cycle time ratio and ensuring that the deposition is removed as quickly as possible. This paper has discussed various approaches to enhance the removal rate of the deposition through chemical and physical approaches. The ability to dynamically

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change the conditions within cycle and cycle to cycle whether it be through the plasma parameters or the use of an additional gas or a combination of both allows more challenging aspect ratios to be etched whilst maintaining a higher etch rate than could be otherwise achieved.

Acknowledgments The authors would like to acknowledge the Process and R&D groups in STS for their contribution to the ongoing development of the DRIE process.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

F. Larmer, R. Schlip, German Patent DE4241045. C. C. Wang, Y. L. Lin, S. K. Lin, C. S. Li, H. K. Hiuang, C. L. Wu, C. S. Chang, Y. H. Wang, Journal Vacuum Science and Technology, B 25 (2), 312–317 (2004). M. J. de Boer, J. G. E. Gardeniers, H. V. Jansen, E. Smulders, M. Gilde, G. Roelofs, J. N. S. Sasserath, M. Elwenspoek, Journal Microelectromechanical Systems, 11(4), 385–401 (2002). B. N. Chapman, Glow Discharge Processes, New York, Wiley Press (1980). www.stsystems.com S. Gomez, R. J. Belen, M. Kiehlbauch, E. S. Aydil , Journal Vacuum Science and Technology, B 22 (3), 893–901 (2004). www.quantemol.com C. B. Labelle, V. M. Donelly, G. R. Bogart, R. L. Opila, A. Kornblit, Journal Vacuum Science and Technology, A 22 (6), 2500-2507 (2004). H. Rhee, H. M. Lee, Y. M. Namkoung C. Kim, H. Chae, Y. W. Kim, Journal Vacuum Science and Technology, B 27 (1), 33–40 (2009). J. Min, G. Lee, J. Lee, S. H. Moon, Journal Vacuum Science and Technology, B 22 (3), 893-901 (2004). M. A. Blauw, T. Zijlstra, E. van der Drift, Journal Vacuum Science and Technology, B 19 (6), 2930–2934 (2001). R. Abdolvand, F. Ayazi, Sensors and Actuators A, 144, 109-116 (2008). M . A. Blauw, G. Craciun, W. G. Sloof, P. J. French, E. van der Drift, Journal Vacuum Science and Tecnology, B 20 (6), 3106–3110 (2002). A. Grill, Cold Plasma in Materials fabrication From Fundamentals to Applications, IEEE Press (1994). Yole Report, MEMS for Mobiles (2006). I. W. Rangelow, Journal Vacuum Science and Technology, A 21 (4), 1550–1562 (2003). J. Hopkins, H. Ashraf, J. K. Bhardwai, A. M. Hynes, I. Johnston, J. N. Shepherd, Proceedings of Materials Research Society Symposium on Materials Science of Microelectromechanical Systems (MEMS) Devices, 546, 63–68 (1999). A. A. Ayon, X. Zhang, R. Khanna, Sensors and Actuators, A 91, 381–385 (2001). J. Bhardwaj, H. Ashraf, B. Khamesphour, J. Hopkins, M. Ryan, D. Haynes, US Patent 6051503.

LOW-TEMPERATURE PROCESSES FOR MEMS DEVICE FABRICATION

JYRKI KIIHAMÄKI*, HANNU KATTELUS, MARTTI BLOMBERG, RIIKKA PUURUNEN, MARI LAAMANEN, PANU PEKKO, JAAKKO SAARILAHTI, HEINI RITALA, AND ANNA RISSANEN VTT Technical Research Centre of Finland, Espoo, Finland

Abstract The high temperatures typical in semiconductor and conventional MEMS fabrication limit the material choices in MEMS structures. This paper reviews some of the low-temperature processes and techniques available for MEMS fabrication and describes some characteristics of these techniques and practical process examples. The techniques described are plasma-enhanced chemical vapour deposition, atomic layer deposition, reactive sputtering, vapour phase hydrofluoric acid etching of low-temperature oxides, and low-temperature wafer bonding. As a practical example of the use of these techniques, the basic characteristics of a MEMS switch and other devices fabricated at VTT are presented.

Keywords: MEMS, thin film technology, fusion bonding, amorphous metals, HF-vapour etching.

1. Introduction The high process temperatures typical in semiconductor [1] and conventional MEMS fabrication [2] limit the material choices in MEMS structures. However, there is wide interest in post-CMOS processing and compatibility with aluminium metallization. Silicon direct bonding with subsequent high-temperature annealing is a standard method for the fabrication of silicon-on-insulator wafers for MEMS and sensor applications. VTT has long experience in low-temperature direct bonding of silicon substrates based on plasma activation of the bonding surfaces, and several activation processes have been developed for our set of plasma tools [3]. Strong bonding can be achieved even at temperatures as low as 200°C, which

______ *

Jyrki Kiihamäki, e-mail: [email protected]

E. Gusev et al. (eds.), Advanced Materials and Technologies for Micro/Nano-Devices, Sensors and Actuators, DOI 10.1007/978-90-481-3807-4_13, © Springer Science + Business Media B.V. 2010

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enables the bonding of wafers of dissimilar temperature coefficients of expansion, or bonding of wafers containing metal structures. This technology has been utilized, for example, in wafer-scale packaging and for the fabrication of MEMS devices with internal vacuum cavities. Silicon dioxide is one cornerstone of silicon-based MEMS fabrication. However, thermal growth of oxides and low-pressure chemical vapour deposition (LPCVD) of oxides typically require higher temperatures than are tolerated in many applications. Plasma-enhanced chemical vapour deposition (PECVD) offers a low-temperature (9 MPa

Solid bond at 280°C

No

Yes

–

–

Solid bond at 350°C

No

Yes

–

–

4.2. INTERCONNECT AND BOND FRAME UNIFORMITY REQUIREMENTS One particular challenge to SLID bonding, and especially at wafer-level, is the lack of a collapsible or reflow process, thus the height uniformity of the electroplated features will significantly affect the bond quality and yield. As mentioned earlier, for many 3D MEMS/ASIC heterogeneous integration applications, a sealing ring is usually required in conjunction with interconnects, which makes the uniformity of the deposited metal thickness even more critical [2]. Electroplating process control together with pattern layout optimization is therefore crucial to increase the overall yield for wafer-level integration and packaging. It is well known that smaller features (such as interconnects) often end up thicker than larger features (such as seal rings) when electroplated. Since there is a linear relationship between current density and electroplated thickness, the height of electroplated features can be estimated by simulating the variation of current densities in a mask [15]. Both seal rings and interconnects must be arranged with optimized areas, and pitch (p), as to minimize any height differences. Figure 7 shows the simulated height differences between interconnects and seal rings for an array of bumps with diameter ranging from 75 to 250 μm together with a seal Interconnect height/Ring height

3.5

1st row; p = 1.2 x W 4th row; p =1.2 x W 1st row; Optimized pitch 4th row; Optimized pitch

3

4th row

2.5

p

2

1st row

1.5

p

1

W

0.5 0.2

0.4

0.6

0.8

1

1.2

Seal ring width = W

Interconnect diameter/Ring width

Figure 7. Simulated height variation for electroplated interconnects and seal ring as a function of bump diameter and pitch. The dashed lines represent permissible height variation for SLID bonding using 5 μm Cu and 3 μm thick Sn bonding features.

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ring 250 μm wide. With an optimized pitch (equal pattern density), interconnects down to 150 μm in diameter can be used in conjunction with a 250 μm wide ring while still remaining within the permissible height variation for SLID bonding.

5. Summary Technological advances within 3D IC integration and packaging continue to push miniaturization and integration of future MEMS-based sensor systems. Integrating MEMS with ASICs in a 3D stack requires a bonding technology suitable for both interconnects and seal rings. SLID bonding of Au–Sn and Cu–Sn which incorporates a 100–200 nm thick protective IMC layer to prevent oxidization of the surfaces at elevated temperatures is investigated. This is particularly important for wafers with released, and free-standing, MEMS devices where a wet pre-cleaning step is not compatible. It is important to keep the protective IMC layer intentionally thin as not to interfere with the inter-diffusion process during bonding. For bonded Cu–Sn samples, with a thin Cu3Sn layer to protect the Cu surface, the measured shear strength is comparable to conventionally SLID bonded interconnects. For Au–Sn samples bonded at 350°C, no bond delamination was observed up to 350°C which is 70°C higher than the eutectic point. Varying the bonding time (in the range of 2–30 min) does not have significant effect on the result. The bonding structure is expected to be stable over time, and not to change composition due to interdiffusion of Au and Sn. The investigated bonding method therefore has potential for high-temperature applications and as a bonding method to tolerate hightemperature processes, such as chip stacking and getter activation, after bonding. Acknowledgements This project is funded by RCN BIA project No. 174320, “3DHMNS – 3D Heterogeneous Micro Nano Systems”. The authors wish to thank Zekija Ramic, Ellen M. Husa and Tormod Vinsand at VUC for laboratory assistance.

References 1. 2. 3. 4.

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3D INTEGRATION OF MEMS AND IC: DESIGN, TECHNOLOGY AND SIMULATIONS

Advanced Processes and Materials MAAIKE M.V. TAKLO, KARI SCHJØLBERG-HENRIKSEN, NICOLAS LIETAER SINTEF ICT, Gaustadalléen 23C, 0373 Oslo, Norway, E-mail: [email protected]

JOSEF PRAINSACK Infineon Technologies, Babenbergerstr. 10, A-8020 Graz, Austria

ANDERS ELFVING SensoNor, Knudsrødveien 7, N-3192 Horten, Norway

JOSEF WEBER, MATTHIAS KLEIN Fraunhofer IZM, Hansastr. 27d, 80686 Munich/Gustav-Meyer-Allee 25, 13355 Berlin, Germany

PETER SCHNEIDER, SVEN REITZ Fraunhofer IIS/EAS, Zeunerstr. 38, 01069 Dresden, Germany

Abstract A 3D integrated silicon stack consisting of two MEMS devices and two IC devices is presented. The MEMS devices are a pressure sensor and a bulk acoustic resonator (BAR). The stack was constructed for a tire pressure monitoring system (TPMS) which was one out of three demonstrators for an EU funded project called e-CUBES. Thermal simulations were performed to check the level of thermo-mechanical stresses induced on the pressure sensor membrane during extreme environmental conditions. Additional simulations were made to calculate the exact temperature on the BAR device during operation as this was important for the operational frequency. This paper presents and discusses the technology choices made for the stacking of the pressure sensor and the BAR. Results are given from simulations, initial short-loop experiments and for the final stacking.

Keywords: MEMS, 3D integration, wafer level packaging, design, wafer bonding, gold stud bump bonding, TSV, simulation.

E. Gusev et al. (eds.), Advanced Materials and Technologies for Micro/Nano-Devices, Sensors and Actuators, DOI 10.1007/978-90-481-3807-4_15, © Springer Science + Business Media B.V. 2010

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1. Introduction Wafer level packaging and 3D integration emerge as an enabling solution for miniaturization of future sensor systems. Densely packaged MEMS devices tightly integrated with the required IC chips and passives can add to the actuating or sensing functionalities of a system without increasing its footprint. However, most MEMS devices available on the market today are not readily prepared for such integration. One of the targets within the EU funded project e-CUBES [1] was to include MEMS devices in miniaturized, 3D integrated sensor nodes. This paper describes the technology for 3D integration of a tire pressure monitoring system (TPMS) with two MEMS devices included: a pressure sensor and a bulk acoustic resonator (BAR). The two main technologies needed for 3D integration are through-silicon/ substrate vias (TSVs) and electrical and mechanical interconnection. Within the integrated circuit (IC) community, substantial research has been carried out in these two areas [2–5]. However, the solutions developed for conventional ICs are not necessarily transferable to MEMS. High TSVs densities with pitches